Tough Problem 1

[Jonmo1]

Never mind, I get it now...

Any number larger than the sqare of the target number cannot be evenly devisible(without a an evenly divisible already previously found).

My original code would countinue needlessly testing if an evenly devisible had not been found prior to the square.


I like the skipping Evens too..

 

[pgc01]

Hi Jonmo

(deleted, you were quicker - I was posting a loop to illustrate what you just said)

 

[Domski]

Okay, I've totally tried and failed!

I mentioned this to a friend of mine who's something of what I consider to be a math guru working for Nat Aus Bank and he's intrigued by both this challenge and that which I posted. If we get a chance next week we'll get together and use his math skills and a bit of my limited Excel knowledge and come back to you. In the meantime I'll just kick his *** at Wii Sports.

After a time maybe a seperate thread with some hints in the right direction rather than a straight solution could help some of us to achieve what we might otherwise have no hope of getting near.

Dom

 

[Andrew Fergus]

This is pretty inefficient but it is purely formula based.

If the formula display isn't working, then here is each unique formula:
B4 : =COUNTIF(E:E,TRUE)
D5 (copy down) : =IF(AND(D4+2<$B$2,D4>3),D4+2,3)
E4 {array formula, copy down} :

=(SUM(IF(MOD(D4,$D$2:D3)=0,1,0))=0) + (SUM(IF(MOD(D3,$D$2:D2)=0,1,0))=0) + (D3>=$B$1)=3

F4 (copy down) : =IF(E4,D3&", " &D4,"")


<script language="JavaScript" src="http://www.interq.or.jp/sun/puremis/colo/popup.js"></script><center><table align="center" cellpadding="0" cellspacing="0"><tbody><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0);" colspan="7" bgcolor="#0c266b"><table width="100%" align="center" border="0"><tbody><tr><td align="left">Microsoft Excel - MakePrime.xls</td><td style="font-size: 9pt; color: rgb(255, 255, 255); font-family: caption;" align="right">___Running: 11.0 : OS = Windows XP </td></tr></tbody></table></td></tr><tr><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); height: 25px;" colspan="7" bgcolor="#d4d0c8"><table valign="MIDDLE" width="100%" align="center" border="0"><tbody><tr><td style="font-size: 10pt; color: rgb(0, 0, 0); font-family: caption;">(F)ile (E)dit (V)iew (I)nsert (O)ptions (T)ools (D)ata (W)indow (H)elp (A)bout</td><td valign="center" align="right"><form name="formCb059465"><input onclick='window.clipboardData.setData("Text",document.formFb543420.sltNb142651.value);' value="Copy Formula" name="btCb290334" type="button"></form></td></tr></tbody></table></td></tr><tr><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0);" colspan="7" bgcolor="white"><table border="0"><tbody><tr><form name="formFb543420"></form><td style="width: 60px;" align="middle" bgcolor="white"><select onchange="document.formFb543420.txbFb965317.value = document.formFb543420.sltNb142651.value" name="sltNb142651"><option value="=COUNTIF(E:E,TRUE)" selected="selected">B4</option><option value="{=(SUM(IF(MOD(D4,$D$2:D3)=0,1,0))=0)+(SUM(IF(MOD(D3,$D$2:D2)=0,1,0))=0)+(D3>=$B$1)=3}">E4</option><option value="=IF(E4,D3&&quot;, " &D4,"")">F4</option><option value="=IF(AND(D4+2<$B$2,D4>3),D4+2,3)">D5</option><option value="{=(SUM(IF(MOD(D5,$D$2:D4)=0,1,0))=0)+(SUM(IF(MOD(D4,$D$2:D3)=0,1,0))=0)+(D4>=$B$1)=3}">E5</option><option value="=IF(E5,D4&&quot;, " &D5,"")">F5</option><option value="=IF(AND(D5+2<$B$2,D5>3),D5+2,3)">D6</option><option value="{=(SUM(IF(MOD(D6,$D$2:D5)=0,1,0))=0)+(SUM(IF(MOD(D5,$D$2:D4)=0,1,0))=0)+(D5>=$B$1)=3}">E6</option><option value="=IF(E6,D5&&quot;, " &D6,"")">F6</option><option value="=IF(AND(D6+2<$B$2,D6>3),D6+2,3)">D7</option><option value="{=(SUM(IF(MOD(D7,$D$2:D6)=0,1,0))=0)+(SUM(IF(MOD(D6,$D$2:D5)=0,1,0))=0)+(D6>=$B$1)=3}">E7</option><option value="=IF(E7,D6&&quot;, " &D7,"")">F7</option><option value="=IF(AND(D7+2<$B$2,D7>3),D7+2,3)">D8</option><option value="{=(SUM(IF(MOD(D8,$D$2:D7)=0,1,0))=0)+(SUM(IF(MOD(D7,$D$2:D6)=0,1,0))=0)+(D7>=$B$1)=3}">E8</option><option value="=IF(E8,D7&&quot;, " &D8,"")">F8</option><option value="=IF(AND(D8+2<$B$2,D8>3),D8+2,3)">D9</option><option value="{=(SUM(IF(MOD(D9,$D$2:D8)=0,1,0))=0)+(SUM(IF(MOD(D8,$D$2:D7)=0,1,0))=0)+(D8>=$B$1)=3}">E9</option><option value="=IF(E9,D8&&quot;, " &D9,"")">F9</option><option value="=IF(AND(D9+2<$B$2,D9>3),D9+2,3)">D10</option><option value="{=(SUM(IF(MOD(D10,$D$2:D9)=0,1,0))=0)+(SUM(IF(MOD(D9,$D$2:D8)=0,1,0))=0)+(D9>=$B$1)=3}">E10</option><option value="=IF(E10,D9&&quot;, " &D10,"")">F10</option><option value="=IF(AND(D10+2<$B$2,D10>3),D10+2,3)">D11</option><option value="{=(SUM(IF(MOD(D11,$D$2:D10)=0,1,0))=0)+(SUM(IF(MOD(D10,$D$2:D9)=0,1,0))=0)+(D10>=$B$1)=3}">E11</option><option value="=IF(E11,D10&&quot;, " &D11,"")">F11</option><option value="=IF(AND(D11+2<$B$2,D11>3),D11+2,3)">D12</option><option value="{=(SUM(IF(MOD(D12,$D$2:D11)=0,1,0))=0)+(SUM(IF(MOD(D11,$D$2:D10)=0,1,0))=0)+(D11>=$B$1)=3}">E12</option><option value="=IF(E12,D11&&quot;, " &D12,"")">F12</option><option value="=IF(AND(D12+2<$B$2,D12>3),D12+2,3)">D13</option><option value="{=(SUM(IF(MOD(D13,$D$2:D12)=0,1,0))=0)+(SUM(IF(MOD(D12,$D$2:D11)=0,1,0))=0)+(D12>=$B$1)=3}">E13</option><option value="=IF(E13,D12&&quot;, " &D13,"")">F13</option><option value="=IF(AND(D13+2<$B$2,D13>3),D13+2,3)">D14</option><option value="{=(SUM(IF(MOD(D14,$D$2:D13)=0,1,0))=0)+(SUM(IF(MOD(D13,$D$2:D12)=0,1,0))=0)+(D13>=$B$1)=3}">E14</option><option value="=IF(E14,D13&&quot;, " &D14,"")">F14</option><option value="=IF(AND(D14+2<$B$2,D14>3),D14+2,3)">D15</option><option value="{=(SUM(IF(MOD(D15,$D$2:D14)=0,1,0))=0)+(SUM(IF(MOD(D14,$D$2:D13)=0,1,0))=0)+(D14>=$B$1)=3}">E15</option><option value="=IF(E15,D14&&quot;, " &D15,"")">F15</option><option value="=IF(AND(D15+2<$B$2,D15>3),D15+2,3)">D16</option><option value="{=(SUM(IF(MOD(D16,$D$2:D15)=0,1,0))=0)+(SUM(IF(MOD(D15,$D$2:D14)=0,1,0))=0)+(D15>=$B$1)=3}">E16</option><option value="=IF(E16,D15&&quot;, " &D16,"")">F16</option><option value="=IF(AND(D16+2<$B$2,D16>3),D16+2,3)">D17</option><option value="{=(SUM(IF(MOD(D17,$D$2:D16)=0,1,0))=0)+(SUM(IF(MOD(D16,$D$2:D15)=0,1,0))=0)+(D16>=$B$1)=3}">E17</option><option value="=IF(E17,D16&&quot;, " &D17,"")">F17</option><option value="=IF(AND(D17+2<$B$2,D17>3),D17+2,3)">D18</option><option value="{=(SUM(IF(MOD(D18,$D$2:D17)=0,1,0))=0)+(SUM(IF(MOD(D17,$D$2:D16)=0,1,0))=0)+(D17>=$B$1)=3}">E18</option><option value="=IF(E18,D17&&quot;, " &D18,"")">F18</option><option value="=IF(AND(D18+2<$B$2,D18>3),D18+2,3)">D19</option><option value="{=(SUM(IF(MOD(D19,$D$2:D18)=0,1,0))=0)+(SUM(IF(MOD(D18,$D$2:D17)=0,1,0))=0)+(D18>=$B$1)=3}">E19</option><option value="=IF(E19,D18&&quot;, " &D19,"")">F19</option><option value="=IF(AND(D19+2<$B$2,D19>3),D19+2,3)">D20</option><option value="{=(SUM(IF(MOD(D20,$D$2:D19)=0,1,0))=0)+(SUM(IF(MOD(D19,$D$2:D18)=0,1,0))=0)+(D19>=$B$1)=3}">E20</option><option value="=IF(E20,D19&&quot;, " &D20,"")">F20</option><option value="=IF(AND(D20+2<$B$2,D20>3),D20+2,3)">D21</option><option value="{=(SUM(IF(MOD(D21,$D$2:D20)=0,1,0))=0)+(SUM(IF(MOD(D20,$D$2:D19)=0,1,0))=0)+(D20>=$B$1)=3}">E21</option><option value="=IF(E21,D20&&quot;, " &D21,"")">F21</option><option value="=IF(AND(D21+2<$B$2,D21>3),D21+2,3)">D22</option><option value="{=(SUM(IF(MOD(D22,$D$2:D21)=0,1,0))=0)+(SUM(IF(MOD(D21,$D$2:D20)=0,1,0))=0)+(D21>=$B$1)=3}">E22</option><option value="=IF(E22,D21&&quot;, " &D22,"")">F22</option><option value="=IF(AND(D22+2<$B$2,D22>3),D22+2,3)">D23</option><option value="{=(SUM(IF(MOD(D23,$D$2:D22)=0,1,0))=0)+(SUM(IF(MOD(D22,$D$2:D21)=0,1,0))=0)+(D22>=$B$1)=3}">E23</option><option value="=IF(E23,D22&&quot;, " &D23,"")">F23</option><option value="=IF(AND(D23+2<$B$2,D23>3),D23+2,3)">D24</option><option value="{=(SUM(IF(MOD(D24,$D$2:D23)=0,1,0))=0)+(SUM(IF(MOD(D23,$D$2:D22)=0,1,0))=0)+(D23>=$B$1)=3}">E24</option><option value="=IF(E24,D23&&quot;, " &D24,"")">F24</option><option value="=IF(AND(D24+2<$B$2,D24>3),D24+2,3)">D25</option><option value="{=(SUM(IF(MOD(D25,$D$2:D24)=0,1,0))=0)+(SUM(IF(MOD(D24,$D$2:D23)=0,1,0))=0)+(D24>=$B$1)=3}">E25</option><option value="=IF(E25,D24&&quot;, " &D25,"")">F25</option><option value="=IF(AND(D25+2<$B$2,D25>3),D25+2,3)">D26</option><option value="{=(SUM(IF(MOD(D26,$D$2:D25)=0,1,0))=0)+(SUM(IF(MOD(D25,$D$2:D24)=0,1,0))=0)+(D25>=$B$1)=3}">E26</option><option value="=IF(E26,D25&&quot;, " &D26,"")">F26</option><option value="=IF(AND(D26+2<$B$2,D26>3),D26+2,3)">D27</option><option value="{=(SUM(IF(MOD(D27,$D$2:D26)=0,1,0))=0)+(SUM(IF(MOD(D26,$D$2:D25)=0,1,0))=0)+(D26>=$B$1)=3}">E27</option><option value="=IF(E27,D26&&quot;, " &D27,"")">F27</option><option value="=IF(AND(D27+2<$B$2,D27>3),D27+2,3)">D28</option><option value="{=(SUM(IF(MOD(D28,$D$2:D27)=0,1,0))=0)+(SUM(IF(MOD(D27,$D$2:D26)=0,1,0))=0)+(D27>=$B$1)=3}">E28</option><option value="=IF(E28,D27&&quot;, " &D28,"")">F28</option></select></td><td width="3%" align="right" bgcolor="#d4d0c8">=</td><td align="left" bgcolor="white"><input size="80" value="=COUNTIF(E:E,TRUE)" name="txbFb965317"></td></tr></tbody></table></td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); background-color: rgb(212, 208, 200);" width="2%" align="middle">
</td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: black; font-family: menu; background-color: rgb(212, 208, 200);" align="middle"><center>A</center></td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: black; font-family: menu; background-color: rgb(212, 208, 200);" align="middle"><center>B</center></td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: black; font-family: menu; background-color: rgb(212, 208, 200);" align="middle"><center>C</center></td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: black; font-family: menu; background-color: rgb(212, 208, 200);" align="middle"><center>D</center></td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: black; font-family: menu; background-color: rgb(212, 208, 200);" align="middle"><center>E</center></td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: black; font-family: menu; background-color: rgb(212, 208, 200);" align="middle"><center>F</center></td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>1</center></td><td style="border-style: solid; border-color: rgb(0, 0, 0) rgb(212, 208, 200) rgb(212, 208, 200) rgb(0, 0, 0); border-width: 0.5pt; font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">START</td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(204, 255, 204); text-align: right;">5</td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: left;">Number</td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">Pair?</td><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">Pair</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>2</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">LIMIT</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(204, 255, 204); text-align: right;">100</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">2</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;"> </td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>3</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">3</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;"> </td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>4</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">PAIRS</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">7</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">5</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>5</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">7</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">TRUE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">5, 7</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>6</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">9</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>7</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">11</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>8</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">13</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">TRUE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">11, 13</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>9</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">15</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>10</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">17</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>11</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">19</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">TRUE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">17, 19</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>12</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">21</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>13</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">23</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>14</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">25</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>15</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">27</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>16</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">29</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>17</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">31</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">TRUE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">29, 31</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>18</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">33</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>19</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">35</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>20</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">37</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>21</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">39</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>22</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">41</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>23</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">43</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">TRUE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">41, 43</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>24</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">45</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>25</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">47</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>26</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">49</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>27</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">51</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-top: 0.5pt solid rgb(0, 0, 0); border-left: 0.5pt solid rgb(0, 0, 0); font-size: 10pt; color: rgb(0, 0, 0); font-family: menu; background-color: rgb(212, 208, 200);" width="2%" align="middle"><center>28</center></td><td style="border-left: 0.5pt solid rgb(0, 0, 0); border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;"> </td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">53</td><td style="border-right: 0.5pt solid rgb(212, 208, 200); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: right;">FALSE</td><td style="border-right: 0.5pt solid rgb(0, 0, 0); border-bottom: 0.5pt solid rgb(212, 208, 200); font-size: 10pt; vertical-align: bottom; color: rgb(0, 0, 0); font-family: Arial; background-color: rgb(255, 255, 255); text-align: center;">
</td></tr><tr><td style="border-style: solid; border-color: rgb(128, 128, 128) rgb(0, 0, 0) rgb(0, 0, 0); border-width: 0.5pt; background-color: rgb(212, 208, 200);" colspan="7"><table valign="TOP" width="100%" align="left"><tbody><tr><td style="border-style: solid; border-color: rgb(128, 128, 128) rgb(0, 0, 0) rgb(0, 0, 0); border-width: 0.5pt; width: 120pt; background-color: rgb(255, 255, 255);" align="left">Sheet1</td><td> </td></tr></tbody></table></td></tr></tbody></table>
[HtmlMaker 2.42] To see the formula in the cells just click on the cells hyperlink or click the Name box
PLEASE DO NOT QUOTE THIS TABLE IMAGE ON SAME PAGE! OTHEWISE, ERROR OF JavaScript OCCUR.


</center>

 

[barry houdini]

Here's a single formula to give the number of pairs, assuming N in A1

=SUM((FREQUENCY(ROW(INDIRECT("5:"&A1+3)),(MMULT((MOD(ROW(INDIRECT("5:"&A1)),TRANSPOSE(ROW(INDIRECT("2:"&A1))))=0)+0,ROW(INDIRECT("2:"&A1))^0)=1)*ROW(INDIRECT("5:"&A1)))=2)+0)

confirmed with CTRL+SHIFT+ENTER

It's very inefficient though and I couldn't get it to calculate for values of N > 5000 without my worksheet crashing

I have a longer, slightly less costly formula but I'm still trying to improve it. I need a way to generate some smaller arrays (especially for the divisor in the MOD function) without compromising the accuracy......

 

[pgc01]

Hi Andrew

I tried your solution and it seems to work ok! It may require, however, several thousands of formulas. Can you, or anyone else, use that idea to come up with a more compact solution?

Cheers

 

[pgc01]

Great formula Barry!!!

If you can make work until 10000, it will be difficult for anyone to come up with a better one. I'm trying also, but my present formula is much (much,much) longer than yours, although it works till the 10000. I won't have much time today but I'll try to make it smaller.

Cheers

 

[sous2817]

This isn't my formula, but a solution I found posted at http://www.cpearson.com/excel/PrimeNumbers.aspx:

The function below will return prime twin if the value in C15 is a prime and either C15-2 or C15+2 is a prime. If C15 is prime but neither C15-2 nor C15+2 is prime, the result is prime. If C15 is not a prime, the result is not prime. Like the formula above, this is an array formula so you must enter it with CTRL SHIFT ENTER. For readability here, the formula is split across several lines. In Excel, you will need to join these lines together.

=IF(OR(C15=1,C15=3),"prime twin",IF(AND((MOD(C15,ROW(INDIRECT("2:"&C15-1)))<>0)),
IF(OR(AND((MOD(C15-2,ROW(INDIRECT("2:"&C15-3)))<>0)),
AND((MOD(C15+2,ROW(INDIRECT("2:"&C15+1)))<>0))),"prime twin","prime"),"not prime"))
This formula will work in Excel 2003 and earlier with numbers up to 65,536. In Excel 2007, it will work with numbers up to 1,048,577. In Excel 2007, you can use the formula below to work with numbers up to 268,435,455.

=IF(OR(C15=1,C15=3),"prime twin",IF(AND((MOD(C15,ROW(INDIRECT
("2:"&INT(SQRT(C15)))))<>0)),IF(OR(AND((MOD(C15-2,ROW(INDIRECT("2:"&
INT(SQRT(C15)))))<>0)),AND((MOD(C15+2,ROW(INDIRECT("2:"&INT(SQRT(C15)))))<>0))),
"prime twin","prime"),"not prime"))

I thought I'd post it here to spur some discussion, as this is way outside of my abilities but makes for great reading!

 

[Andrew Fergus]

Interesting solution but I think it contains an error in the very first part : OR(C15=1,C15=3),"prime twin"

1 is not actually a prime number!!
Andrew

 

[fairwinds]

I need a way to generate some smaller arrays (especially for the divisor in the MOD function) without compromising the accuracy......

Hi,

This seems to work for me, using only array up to the square root of n.

{=SUM(--((FREQUENCY(((ROW(INDIRECT("5:"&A1-2))=TRANSPOSE(ROW(INDIRECT("2:"&INT(SQRT(A1))))))+(ROW(INDIRECT("7:"&A1))=TRANSPOSE(ROW(INDIRECT("2:"&INT(SQRT(A1))))))+MOD(ROW(INDIRECT("5:"&A1-2)),TRANSPOSE(ROW(INDIRECT("2:"&INT(SQRT(A1))))))*MOD(ROW(INDIRECT("7:"&A1)),TRANSPOSE(ROW(INDIRECT("2:"&INT(SQRT(A1))))))>0)*ROW(INDIRECT("5:"&A1-2)),ROW(INDIRECT("4:"&A1))))-INT(SQRT(A1))=-1))*(A1>6)-(A1=8)}