CPAP-2

The Largest Known Cousin Primes (two primes separated by 4)
 (with at least 10,000 digits)
Primes Digits When Discoverer(s)
954589277 • (2332267 − 2110758) + 2221511 − 3 + d, d = 0, 4 100032 21 Apr 2025 Serge Batalov, PolySieve, OpenPFGW
8797170843 • (2317583 + 2190552) + 2127033 − 1 + d, d = 0, 4 95612 3 Feb 2025 Serge Batalov, PolySieve, OpenPFGW
(74018908351  •  (2190738 − 1) + 4)  • 295369 − 1 + d, d = 0, 4 86138 16 Dec 2024 Serge Batalov, PolySieve, OpenPFGW
(29571282950  •  (2190738 − 1) − 4)  • 295369 − 1 + d, d = 0, 4 86138 7 Dec 2024 Serge Batalov, PolySieve, OpenPFGW
(78866031017  •  (2166678 − 1) − 4)  • 283339 − 3 + d, d = 0, 4 75274 25 Nov 2024 Serge Batalov, PolySieve, OpenPFGW
(90704749637  •  (2110503 − 1) + 2)  • 2110504 − 3 + d, d = 0, 4 66541 4 Nov 2024 Serge Batalov, PolySieve, OpenPFGW
(42550837315  •  (2110503 − 1) + 1)  • 2110505 − 3 + d, d = 0, 4 66541 6 Nov 2024 Serge Batalov, PolySieve, OpenPFGW
29055814795 • (2172486 − 286243) + 286245 − 3 + d, d = 0, 4 51934 3 May 2022 Serge Batalov, OpenPFGW, BLS-proof
(520461 • 255931 + 1) • (43439253939 • (520461 • 255931 − 1)2 − 3) + 1 + d, d = 0, 4 50539 26 May 2021 Peter Kaiser, PrimeForm, OpenPFGW, BLS-proof
4404139952163 • 267002 − 5 + d, d = 0, 4 20183 11 Jul 2024 Serge Batalov, PolySieve, OpenPFGW, CM
4111286921397 • 266420 + 1 + d, d = 0, 4 20008 23 Apr 2019 Peter Kaiser, PolySieve, LLR, Primo
6521953289619 • 255555 − 5 + d, d = 0, 4 16737 30 Apr 2013 Peter Kaiser, Primo
56667641271 • 244441 + 1 + d, d = 0, 4 13389 2 Apr 2022 Stephan Schöler, NewPGen, OpenPFGW;
Oliver Kruse, Primo
(9771919142 • ((53238 • 7879#)2 − 1) + 2310) • 53238 • 7879# / 385 + 1 + d, d = 0, 4 10154 Nov 2005 Torbjörn Alm, Micha Fleuren &
Jens Kruse Andersen

The Largest Known Sexy Prime Pairs (two primes separated by 6)
 (with at least 10,000 digits)
PrimesDigits YearDiscoverer(s)
7977227425 • (2368352 − 2257849) + 2110505 − 5 + d, d = 0, 6 110895 11 May 2025 Serge Batalov, PolySieve, OpenPFGW
(84741735735 • (2190738 − 1) + 4) • 295369 − 1 + d, d = 0, 6 86138 21 Dec 2024 Serge Batalov, PolySieve, OpenPFGW
(16472224158 • (2166678 − 1) − 1) • 283341 − 5 + d, d = 0, 6 75274 23 Nov 2024 Serge Batalov, PolySieve, OpenPFGW
(50573264686 • (2110503 − 1) + 1) • 2110505 − 5 + d, d = 0, 6 66541 8 Nov 2024 Serge Batalov, PolySieve, OpenPFGW
11922002779 • (2172486 − 286243) + 286245 − 5 + d, d = 0, 6 51934 3 May 2022 Serge Batalov, OpenPFGW BLS-proof
(520461 • 255931 + 1) • (98569639289 • (520461 • 255931 − 1)2 − 3) − 1 + d, d = 0, 6 50539 2 Oct 2019 Serge Batalov
(187983281 • 251478 + 4) • (5 • 251478 − 1) + 5 + d, d = 0, 6 31002 24 Apr 2019 Serge Batalov, BLS-proof
(153528880 • (1369 • 246028 − 1) + 6) • 37 • 223014 − 1 + d, d = 0, 6 20797 22 Apr 2019 Serge Batalov, BLS-proof
2683143625525 • 235176 + 7, d = 0, 6 10602 29 Dec 2019 Gerd Lamprecht, Norman Luhn, Primo
2683143625525 • 235176 + 1, d = 0, 6 10602 29 Dec 2019 Gerd Lamprecht, Norman Luhn, Primo
59056921173 • 234030 + 1, d = 0, 6 10255 7 Jun 2022 Greg Childers, CM
18416522281203 • 233222 + 5, d = 0, 6 10015 23 Jan 2020 Peter Kaiser, Primo
18416522281203 • 233222 − 1, d = 0, 6 10015 23 Jan 2020 Peter Kaiser, Primo