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{{Proth prime
 
{{Proth prime
 
|Pk=7
 
|Pk=7
 +
|Pb=2
 +
|PCount=43
 
|PNash=2144
 
|PNash=2144
−
|PMaxn=6000000
+
|PMaxn=9000000
−
|PDate=2008-11-14
+
|PDate=2022-07-21
 
|PReserved=
 
|PReserved=
 +
|PMultiRes=
 
|PNlist=
 
|PNlist=
−
2
+
2;T:G
−
4
+
4;T:G
−
6;C:Divides: GF(4,10)
+
6;T:G;C:{{NCu|+|2|6}}, {{NWi|MP|8|2}}
−
14;C:Divides: F(12)
+
14;T:G;C:{{NCu|4|7}}, {{NCu|+|2|13}}
−
20;C:Divides: GF(19,5)
+
20;T:GS
−
26
+
26;T:G
−
50;C:Divides: GF(49,3)
+
50;T:G
−
52;C:Divides: GF(51,12)
+
52;T:G
−
92;C:Divides: GF(91,12)
+
92;T:G
−
120;C:Divides: F(117)
+
120;T:G;C:{{NWi|MP|8|40}}
−
174;C:Divides: GF(171,5)
+
174;T:G;C:{{NWi|MP|8|58}}
−
180;C:Divides: GF(179,10)
+
180;T:G;C:{{NWi|MP|8|60}}
−
190
+
190;T:G
−
290;C:Divides: F(284)
+
290;T:G
−
320;C:Divides: F(316), GF(319,3), GF(319,6), GF(319,12)
+
320;T:G
−
390;C:Divides: GF(389,6)
+
390;T:GS;C:{{NWi|MP|8|130}}
−
432;C:Divides: GF(431,6)
+
432;T:G;C:{{NWi|MP|8|144}}
−
616;C:Divides: GF(615,10)
+
616;T:G
−
830;C:Divides: GF(828,5), GF(829,6)
+
830;T:G
−
1804;C:Divides: GF(1803,5), GF(1803,12)
+
1804;T:G
−
2256
+
2256;T:G;C:{{NWi|MP|8|752}}
−
6614;37379;C:Divides: GF(6612,10)
+
6614;37379;T:G
−
13496;27240
+
13496;27240;T:G
−
15494;26187
+
15494;26187;T:G
−
16696;25162;C:Divides: GF(16695,5)
+
16696;25162;T:G
−
22386;21739;C:Divides: GF(22385,6)
+
22386;21739;T:G;C:{{NWi|MP|8|7462}}
−
54486;11363;C:Divides: GF(54485,3)
+
54486;11363;T:G;C:{{NWi|MP|8|18162}}
−
88066;6342
+
88066;6342;T:G
−
95330;5701;C:Divides: F(95328), GF(95329,3), GF(95329,6), GF(95329,12)
+
95330;5701;T:G
−
207084;421
+
207084;421;T:G;C:{{NWi|MP|8|69028}}
−
283034;246
+
283034;246;T:G
−
561816;65142;C:Divides: GF(561815,5), GF(561815,6)
+
561816;65142;T:G;C:{{NWi|MP|8|187272}}
−
804534;67632;C:Divides: GF(804533,12)
+
804534;67632;T:G;C:{{NWi|MP|8|268178}}
−
811230;62795;C:Divides: GF(811228,5)
+
811230;62795;T:G;C:{{NWi|MP|8|270410}}
−
1491852;73590;C:Divides: GF(1491851,6)
+
1491852;73590;T:G;C:{{NWi|MP|8|497284}}
−
2139912;80448;C:Divides: GF(2139911,12)
+
2139912;80448;T:G;C:{{NWi|MP|8|713304}}
−
2167800;80047;C:Divides: F(2167797), GF(2167799,5), GF(2167799,10)
+
2167800;80047;T:G;C:{{NWi|MP|8|722600}}
−
2915954;85126;C:Divides: GF(2915953,12)
+
2915954;85126;T:G
−
3015762;83806
+
3015762;83806;T:G;C:{{NWi|MP|8|1005254}}
−
3511774;85758;C:Divides: GF(3511773,6)
+
3511774;85758;T:G
−
|PRemarks=
+
5775996;110070;T:G;C:{{NWi|MP|8|1925332}}
 +
18233956;131289;T:G
 +
20267500;134192;T:G
 +
|PRemarks=The {{OEIS|l|A032353}}<br>See also {{NWi|MP|8|n}}
 
}}
 
}}
 +
==History==
 +
{{HistF|2022-07-21|20267500|Ryan Propper}}
 +
{{HistC|2021-04-01|6000000-9000000|PrimeGrid Fermat Divisor Search|P#8778#149792}}
 +
{{HistC|2020-10-12|[[GF_Divisor 7 18233956|GF Divisors]] for {{Vn}} &#61; 18233956|Gary B. Gostin|559634}}
 +
{{HistF|2020-10-01|18233956|Ryan Propper|558592}}
 +
{{HistC|?|6000000|PrimeGrid Proth Prime Search}}
 +
{{HistF|2012-11-10|5775996|Martyn Elvy,PrimeGrid Proth Prime Search}} ([http://www.primegrid.com/download/PPS-5775996.pdf Official announcement])
 +
{{HistF|2008-11-14|3511774|Curtis Cooper}}
 +
{{HistF|2008-06-09|2915954|Curtis Cooper}}
 +
{{HistF|2008-01-30|3015762|Curtis Cooper}}
 +
{{HistF|2007-05-12|2139912|Curtis Cooper}}
 +
{{HistF|2007-04-15|2167800|Curtis Cooper}}
 +
{{HistF|2005-03-02|1491852|Shoichiro Yamada,Satoshi Noda,Takahiro Nohara}}
 +
{{HistF|2003-12-10|804534|Kevin Odermatt}}
 +
{{HistF|2003-06-15|561816|Payam Samidoost}}
 +
{{HistF|2002-12-18|811230|Payam Samidoost}}
 +
{{HistF|1998-10-01|283034|Jeffrey Young}}
 +
{{HistF|1998-07-08|207084|Skip Key}}
 +
{{HistF|1995-08|95330|Jeffrey Young}}
 +
{{HistF|1995-08|88066|Jeffrey Young}}
 +
{{HistF|1992-10-01|16696|Harvey Dubner}}
 +
{{HistF|1992|22386|Harvey Dubner}}
 +
{{HistF|1987|54486|Jeffrey Young}}
 +
{{HistF|1984|15494|Wilfrid Keller}}
 +
{{HistF|1984|13496|Wilfrid Keller}}
 +
{{HistC|1979|1500-8000|Gordon V. Cormack,Hugh C. Williams}}
 +
{{HistF|1979|1804|Gordon V. Cormack,Hugh C. Williams}}
 +
{{HistF|1979|2256|Gordon V. Cormack,Hugh C. Williams}}
 +
{{HistF|1979|6614|Gordon V. Cormack,Hugh C. Williams}}

Latest revision as of 00:50, 27 September 2024

Current data

k , b : 7 , 2
Count : 43
Nash : 2144
Max n : 9,000,000
Date : 2022-07-21
2[1], 4[2], 6[3], 14[4], 20[5], 26[6], 50[7], 52[8], 92[9], 120[10], 174[11], 180[12], 190[13], 290[14], 320[15], 390[16], 432[17], 616[18], 830[19], 1804[20], 2256[21], 6614[22], 13496[23], 15494[24], 16696[25], 22386[26], 54486[27], 88066[28], 95330[29], 207084[30], 283034[31], 561816[32], 804534[33], 811230[34], 1491852[35], 2139912[36], 2167800[37], 2915954[38], 3015762[39], 3511774[40], 5775996[41], 18233956[42], 20267500[43]
Remarks :
The sequence A032353 in OEIS
See also Williams 7•8n+1

Notes

  1. ↑ Is GF Divisor of xGF(1,5,2) [+3]
  2. ↑ Is GF Divisor of xGF(2,6,5) [+4]
  3. ↑ Is GF Divisor of xGF(4,7,2) [+6], Near Cullen 7•26+1, Williams 7•82+1
  4. ↑ Is GF Divisor of F(12) [+6], Cullen 7•47+1, Near Cullen 14•213+1
  5. ↑ Is GF Divisor of xGF(19,3,2) [+8], Sophie Germain n=20
  6. ↑ Is GF Divisor of xGF(25,4,3) [+5]
  7. ↑ Is GF Divisor of GF(49,3) [+3]
  8. ↑ Is GF Divisor of xGF(51,7,5) [+5]
  9. ↑ Is GF Divisor of xGF(91,5,2) [+5]
  10. ↑ Is GF Divisor of F(117) [+4], Williams 7•840+1
  11. ↑ Is GF Divisor of GF(171,5) [+6], Williams 7•858+1
  12. ↑ Is GF Divisor of xGF(176,7,4) [+4], Williams 7•860+1
  13. ↑ Is GF Divisor of xGF(189,4,3) [+5]
  14. ↑ Is GF Divisor of F(284) [+4]
  15. ↑ Is GF Divisor of F(316) [+16]
  16. ↑ Is GF Divisor of GF(389,6) [+4], Sophie Germain n=390, Williams 7•8130+1
  17. ↑ Is GF Divisor of GF(431,6) [+4], Williams 7•8144+1
  18. ↑ Is GF Divisor of GF(610,7) [+5]
  19. ↑ Is GF Divisor of GF(828,5) [+5]
  20. ↑ Is GF Divisor of GF(1803,5) [+6]
  21. ↑ Is GF Divisor of xGF(2255,4,3) [+5], Williams 7•8752+1
  22. ↑ Is GF Divisor of xGF(6613,3,2) [+3]
  23. ↑ Is GF Divisor of xGF(13495,3,2) [+5]
  24. ↑ Is GF Divisor of xGF(15493,3,2) [+4]
  25. ↑ Is GF Divisor of GF(16695,5) [+4]
  26. ↑ Is GF Divisor of GF(22385,6) [+4], Williams 7•87462+1
  27. ↑ Is GF Divisor of GF(54485,3) [+7], Williams 7•818162+1
  28. ↑ Is GF Divisor of xGF(88065,3,2) [+6]
  29. ↑ Is GF Divisor of F(95328) [+25]
  30. ↑ Is GF Divisor of xGF(207083,4,3) [+4], Williams 7•869028+1
  31. ↑ Is GF Divisor of xGF(283033,6,5) [+4]
  32. ↑ Is GF Divisor of GF(561815,5) [+3], Williams 7•8187272+1
  33. ↑ Is GF Divisor of xGF(804531,5,4) [+4], Williams 7•8268178+1
  34. ↑ Is GF Divisor of GF(811228,5) [+5], Williams 7•8270410+1
  35. ↑ Is GF Divisor of GF(1491851,6) [+5], Williams 7•8497284+1
  36. ↑ Is GF Divisor of xGF(2139911,5,2) [+5], Williams 7•8713304+1
  37. ↑ Is GF Divisor of F(2167797) [+11], Williams 7•8722600+1
  38. ↑ Is GF Divisor of xGF(2915951,5,2) [+6]
  39. ↑ Is GF Divisor of xGF(3015759,5,2) [+3], Williams 7•81005254+1
  40. ↑ Is GF Divisor of GF(3511773,6) [+5]
  41. ↑ Is GF Divisor of xGF(5775995,5,4) [+4], Williams 7•81925332+1
  42. ↑ Is GF Divisor of F(18233954) [+9]
  43. ↑ Is GF Divisor of xGF(20267499,7,6) [+6]

History

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