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.

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 × 2¹⁶³⁵² -1, twin prime record, November, 1994; 4932 decimal digits

157324389 × 2¹⁶³⁵² -1, Sophie Germain prime record, February, 1995; 4931 decimal digits

470943129 × 2¹⁶³⁵² -1, Sophie Germain prime record, February, 1995; 4932 decimal digits

242206083 × 2³⁸⁸⁸⁰ -1, twin prime record, November, 1995; 11713 decimal digits

2375063906985 × 2¹⁹³⁸⁰ -1, Sophie Germain prime record, December, 1995; 5847 digits

4610194180515 × 2⁵⁰⁵⁶ -1, combined record: twin and Sophie Germain prime, January, 1996; 1535 digits

(235 × 2¹⁸⁴⁰⁰)⁴ +1, largest known prime having the form n⁴ +1, found in 1996; 22166 digits

The Waring constant g(k) = + 2^k - 2 for k 5 × 2³⁰; 1995.

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

871892617365 × 2⁴⁸⁰⁰⁰ -1, twin prime record, January, 2000; 14462 decimal digits

2230907354445 × 2⁴⁸⁰⁰⁰ -1, twin prime record, January, 2000; 14462 decimal digits

2409110779845 × 2⁶⁰⁰⁰⁰ -1, twin prime record, January, 2000; 18075 decimal digits

3714089895285 × 2⁶⁰⁰⁰⁰-1, Sophie Germain prime record, March, 2000; 18075 decimal digits

4648619711505 × 2⁶⁰⁰⁰⁰ -1, twin prime record, March, 2000; 18075 decimal digits

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

16869987339975 × 2¹⁷¹⁹⁶⁰ -1, twin prime record, September, 2005; 51779 decimal digits

137211941292195 × 2¹⁷¹⁹⁶⁰ -1, Sophie Germain prime record, May, 2006; 51780 decimal digits

100314512544015 × 2¹⁷¹⁹⁶⁰ -1, twin prime record, Jun, 2006; 51780 decimal digits

194772106074315 × 2¹⁷¹⁹⁶⁰ -1, twin prime record, Jun, 2006; 51780 decimal digits

620366307356565 × 2²⁵³⁸²⁴ -1, Sophie Germain prime record, November, 2009; 76424 decimal digits

648621027630345 × 2²⁵³⁸²⁴ -1, Sophie Germain prime record, November, 2009; 76424 decimal digits

Up-to-date list of prime records