Robert W Smith Homepage

Primoproth Records to date

***Largest primes of the form p#.2^n - 1***
Rank	p#	n	digits	discovered by	date
1	23#	311147	93673	Robert Smith	10.2002
1	23#	289258	87084	Robert Smith	9.2002
1	23#	257138	77415	Robert Smith	8.2002
4	23#	210760	63454	Robert Smith	6.2002
5	23#	209564	63094	Robert Smith	6.2002
6	23#	195312	58828	Robert Smith	5.2002
7	23#	183719	55314	Robert Smith	5.2002
8	23#	178050	52080	Robert Smith	5.2002
9	3#	164986	49667	Wilfrid Keller & Ingo Buechel	1999
10	3#	155929	46941	Wilfrid Keller & Ingo Buechel	1999
11	23#	146075	43982	Robert Smith	4.2002
12	23#	142529	42914	Robert Smith	4.2002
13	23#	141785	42690	Robert Smith	4.2002
14	23#	140625	42341	Robert Smith	4.2002
15	23#	138973	41844	Robert Smith	4.2002
16	23#	125491	37785	Robert Smith	3.2002
17	3#	123629	37217	Wilfrid Keller & Ingo Buechel	1999
18	23#	120717	36348	Robert Smith	3.2002
19	23#	109725	33039	Robert Smith	3.2002
20	3#	97063	29220	Wilfrid Keller & Ingo Buechel	1999
21	5#	91457	27533	Michael Graef	1999
22	3#	88170	26543	Wilfrid Keller & Ingo Buechel	1999
23	23#	86463	26037	Robert Smith	2.2002
24	3#	85686	25792	Wilfrid Keller and Ingo Buechel	1998
25	19#	85518	25751	Robert Smith	10.2002
26	23#	84796	25535	Robert Smith	2.2002
27	19#	82994	24991	Robert Smith	10.2002
28	13#	80887	24354	Robert Smith	6.2002
29	3#	80329	24183	Wilfrid Keller and Ingo Buechel	1998
30	23#	77525	23346	Robert Smith	2.2002

Largest primes of the form p#.2^n + 1
Rank p# n digits discovered by date

1 3# 916772 275977 John Cosgrave 2001

2 5# 403928 121596 Payam Samidoost 2002

3 3# 382448 115130 John Cosgrave 1999

4 3# 303092 91241 Jeffrey Young 1998

5 5# 300487 90458 Payam Samidoost 2002

6 3# 213320 64217 Jeffrey Young 1997

7 7# 200711 60423 Payam Samidoost 2001

8 5# 184289 55478 Jeffrey Young 1998

9 3# 157168 47314 Jeffrey Young 1995

10 7# 133442 40173 Manfred Toplic 1998

11 23# 122530 36894 Robert Smith 9.2002

12 23# 121781 36669 Robert Smith 9.2002

13 11# 119773 36059 Hans Overmann 4.2002

14 11# 118370 35637 Hans Overmann 4.2002

15 373# 100186 30308 Torbjorn Alm 5.2002

16 373# 96453 29035 Torbjorn Alm 5.2002

17 11# 95798 28842 Hans Overmann 2001

18 373# 95126 28784 Torbjorn Alm 5.2002

19 373# 93476 28288 Torbjorn Alm 5.2002

20 373# 93242 28217 Torbjorn Alm 5.2002

21 47# 90499 27261 Torbjorn Alm 6.2002

22 23# 90093 27130 Goran Axelsson 2.2002

23 373# 88129 26678 Torbjorn Alm 5.2002

24 7# 87230 26262 Manfred Toplic 1998

25 28513# 45945 26109 Henri Lifchitz 12.1999

26 373# 86127 26075 Torbjorn Alm 5.2002

27 23# 85811 25841 Robert Smith 9.2002

28 67# 82083 24735 Robert Smith 10.2002

29 67# 80825 24356 Robert Smith 10.2002

30 3# 80189 24141 Jeffrey Young 1995

Most productive series..largest number of primes found
Rank p# +/- primes n checked p/ln(n)

1 23# - 104 300674 8.24

2 67# + 103 85703 9.07

3 251# + 99 65596 8.93

4 89# + 96 61600 8.70

5 373# + 94 107700 8.11

6 47# + 91 90800 7.97

7 509# - 90 58800 8.20

8 193# + 88 40000 8.30

9 139# + 87 50000 8.04

10 491# + 86 50000 7.95

Largest Sophie Germain primes..both p#.2^n-1 and p#.2^(n+1)-1 are prime
Rank p# n digits discovered by date

1 8053# 69 3460 Robert Smith 10.2002

2 7823# 31 3276 Robert Smith 10.2002

3 631# 6964 2358 Dirk Augustin 4.2002

4 431# 7045 2295 Dirk Augustin 4.2002

5 457# 6106 2026 Dirk Augustin 4.2002

6 1061# 5104 1982 Dirk Augustin 4.2002

7 641# 5316 1865 Dirk Augustin 4.2002

8 311# 4303 1421 Robert Smith 3.2002

9 163# 4346 1373 Robert Smith 3.2002

10 2953# 1336 1336 Robert Smith 9.2002

Largest Cunningham Chains of the 1st kind, length 3..p#.2^n-1, p#.2^(n+1)-1 and p#.2^(n+2)-1 are prime
Rank p# n digits discovered by date

1 383# 102 187 Sander Hoogendoorn 5.2002

2 167# 356 174 Robert Smith 3.2002

3 157# 15 69 Robert Smith 3.2002

4 127# 9 52 Robert Smith 3.2002

5 29# 41 23 Robert Smith 2.2002

Cunningham Chains of the 1st kind, length 4 .. p#.2^n-1, p#.2^(n+1)-1, p#.2^(n+2)-1 and p#.2^(n+3)-1 are prime
Rank p# n digits discovered by date

1 227# 29 98 Robert Smith 3.2002

2 3# 1 2 ?? ??

Largest Cunningham Chains of the 2nd kind, length 2..both p#.2^n+1 and p#.2^(n+1)+1 are prime
Rank p# n digits discovered by date

1 13# 23869 7190 Jeffrey Young 1993

2 59# 13965 4226 Torbjorn Alm 5.2002

3 431# 6336 2082 Dirk Augustin 5.2002

4 199# 4819 1533 Robert Smith 3.2002

5 307# 2216 790 Robert Smith 3.2002

6 373# 1773 683 Torbjorn Alm 4.2002

7 103# 2102 674 Robert Smith 3.2002

8 269# 1550 575 Robert Smith 3.2002

9 431# 1306 568 Henri Lifchitz 1.1999

10 401# 1223 532 Torbjorn Alm 4.2002

Cunningham Chains of the 2nd kind, length 3..both p#.2^n+1 and p#.2^(n+1)+1 are prime
Rank p# n digits discovered by date

1 37# 8 33 Robert Smith 2.2002

2 13# 2 7 ?? ??

Cunningham Chains of the 2nd kind, length 4..p#.2^n+1, p#.2^(n+1)+1, p#.2^(n+2)+1 and p#.2^(n+3)+1 are prime
Rank p# n digits discovered by date

1 41# 9 16 Robert Smith 2.2002

2 29# 8 14 Robert Smith 2.2002

3 11# 16 10 ?? ??

4 11# 0 5 ?? ??

Twin Primes..p#.2^n+1 and p#.2^n-1 are prime
Rank p# n digits discovered by date

1 1667# 9607 3607 Didier Boivin 6.2002

2 443# 10285 3279 Mark Rodenkirch 5.2002

3 1481# 8641 3221 Didier Boivin 6.2002

4 431# 6337 2082 Dirk Augustin 5.2002

5 1289# 4700 1956 Didier Boivin 5.2002

6 1697# 3113 1656 Didier Boivin 5.2002

7 1327# 3420 1596 Didier Boivin 5.2002

8 1129# 3575 1566 Didier Boivin 5.2002

9 223# 4582 1466 Robert Smith 3.2002

10 947# 3246 1372 Didier Boivin 5.2002

Bi Twin.. p#.2^n+/-1 and p#.2^(n+1)+/-1 are prime
Rank p# n digits discovered by date

1 71# 189 84 Henri Lifchitz 1.1999

2 137# 76 76 Didier Boivin 5.2002

***Most productive series..largest number of primes found***
Rank	p#	+/-	primes	n checked	p/ln(n)
1	23#	-	104	300674	8.24
2	67#	+	103	85703	9.07
3	251#	+	99	65596	8.93
4	89#	+	96	61600	8.70
5	373#	+	94	107700	8.11
6	47#	+	91	90800	7.97
7	509#	-	90	58800	8.20
8	193#	+	88	40000	8.30
9	139#	+	87	50000	8.04
10	491#	+	86	50000	7.95

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Last Updated October 19, 2002