World records in computational number theory

Our joint work with Prof. Dr. Karl-Heinz Indlekofer in this field started in 1992. I worked in his research group from 1992 until 1997 as a project manager. During this period I designed most of the programs developed by the research group, coded and implemented approximately 70% of them. This highly optimised SuperSPARC assembly code was used in cooperation to obtain new records in 2000. In 2005 a completely redesigned and rewritten new code has been used.

Record List

A prime p is a twin prime if p+2 is prime as well. A prime p is a Sophie Germain prime if 2p+1 is prime as well.

Records by Karl-Heinz Indlekofer and Antal Járai:

697053813 ×
2^{16352} -1, twin prime record, November, 1994; 4932 decimal digits

157324389 ×
2^{16352} -1, Sophie Germain prime record, February, 1995; 4931 decimal digits

470943129 ×
2^{16352} -1, Sophie Germain prime record, February, 1995; 4932 decimal digits

242206083 ×
2^{38880} -1, twin prime record, November, 1995; 11713 decimal digits

2375063906985 ×
2^{19380} -1, Sophie Germain prime record, December, 1995; 5847 digits

4610194180515 ×
2^{5056} -1, combined record: twin and Sophie Germain prime, January, 1996; 1535 digits

(235 ×
2^{18400})^{4} +1, largest known prime having the form n^{4} +1, found in 1996; 22166 digits

The Waring constant *g*(*k*) = + 2* ^{k}* -
2 for

Records by Karl-Heinz Indlekofer, Antal Járai and Heinz-Georg Wassing:

871892617365 ×
2^{48000} -1, twin prime record, January, 2000; 14462 decimal digits

2230907354445 ×
2^{48000} -1, twin prime record, January, 2000; 14462 decimal digits

2409110779845 ×
2^{60000} -1, twin prime record, January, 2000; 18075 decimal digits

3714089895285 ×
2^{60000}-1, Sophie Germain prime record, March, 2000; 18075 decimal digits

4648619711505 ×
2^{60000} -1, twin prime record, March, 2000; 18075 decimal digits

Records by Tímea Csajbók, Gábor Farkas, Antal Járai, Zoltán Járai and János Kasza:

16869987339975 ×
2^{171960} -1, twin prime record, September, 2005; 51779 decimal digits

137211941292195 ×
2^{171960} -1, Sophie Germain prime record, May, 2006; 51780 decimal digits

100314512544015 ×
2^{171960} -1, twin prime record, Jun, 2006; 51780 decimal digits

194772106074315 ×
2^{171960} -1, twin prime record, Jun, 2006; 51780 decimal digits

620366307356565 ×
2^{253824} -1, Sophie Germain prime record, November, 2009; 76424 decimal digits

648621027630345 ×
2^{253824} -1, Sophie Germain prime record, November, 2009; 76424 decimal digits