go back

CPAP-2

A CPAP-2 is by definition any pair of consecutive primes.
There are infinitely many primes and thus infinitely many CPAP-2.
On this page, I collected some largest known Prime Twins, Cousin Primes, Sexy Prime Pairs & largest known gap between two proven primes.
Only proved primes are allowed.

The Largest Known Twin Primes (two primes separated by 2)

PrimesDigitsYear Discoverer(s)
2996863034895 · 21290000 ± 1
388342
19 Sep 2016
Tom Greer, TwinGen, PrimeGrid, LLR
3756801695685 · 2666669 ± 1
200700
26 Dec 2011
Timothy Winslow, TwinGen, PrimeGrid, LLR
65516468355 · 2333333 ± 1
100355
15 Aug 2009
Peter Kaiser, NewPGen, PrimeGrid, TPS, LLR
160204065 · 2262148 ± 1
78923
8 Jul 2021
Erwin Doescher, LLR
12770275971 · 2222225 ± 1
66907
4 Jul 2017
Bo Tornberg, TwinGen, LLR
12599682117 · 2211088 ± 1
63554
22 Feb 2022
Michael Kwok, PSieve, LLR
12566577633 · 2211088 ± 1
63554
22 Feb 2022
Michael Kwok, PSieve, LLR
70965694293 · 2200006 ± 1
60219
2 Apr 2016
S. Urushihata
66444866235 · 2200003 ± 1
60218
2 Apr 2016
S. Urushihata
4884940623 · 2198800 ± 1
59855
3 Jul 2015
Michael Kwok, PSieve, LLR

The Largest Known Cousin Primes (two primes separated by 4)

(with at least 10,000 digits)

PrimesDigits Year Discoverer(s)
29055814795 · (2172486 - 286243) + 286245 - 3 + d, d = 0, 4 51934 2022 Serge Batalov, OpenPFGW BLS-proof
(520461 · 255931 + 1) · (43439253939 · (520461 · 255931 - 1)2 - 3) + 1 + d, d = 0, 4 50539 2021 Peter Kaiser, PrimeForm, OpenPFGW BLS-proof
4111286921397 · 266420 + 1 + d, d = 0, 4 20008 2019 Peter Kaiser, Polysieve, LLR, Primo
6521953289619 · 255555 - 5 + d, d = 0, 4 16737 2013 Peter Kaiser, Primo
56667641271 · 244441 + 1 + d, d = 0, 4 13389 2022 Stephan Schöler, NewPGen, OpenPFGW; Oliver Kruse, Primo
(9771919142 · ((53238 · 7879#)2 - 1) + 2310) · 53238 · 7879# / 385 + 1 + d, d = 0, 4 10154 2005 T. Alm, M. Fleuren, and J. K. Andersen

The Largest Known Sexy Prime Pairs (two primes separated by 6)

(with at least 10,000 digits)

PrimesDigits YearDiscoverer(s)
11922002779 · (2172486 - 286243) + 286245 - 5 + d, d = 0, 6 51934 2022 Serge Batalov, OpenPFGW BLS-proof
(520461 · 255931 + 1) · (98569639289 · (520461·255931 - 1)2 - 3) - 1 + d, d = 0, 6 50539 2019 Serge Batalov
(187983281 · 251478 + 4) · (5 · 251478 - 1) + 5 + d, d = 0, 6 31002 2019 Serge Batalov, BLS-proof
(153528880 · (1369 · 246028 - 1) + 6) · 37 · 223014 - 1 + d, d = 0, 6 20797 2019 Serge Batalov, BLS-proof
2683143625525 · 235176 + 7, d = 0, 6 10602 2019 Gerd Lamprecht, Norman Luhn, Primo
2683143625525 · 235176 + 1, d = 0, 6 10602 2019 Gerd Lamprecht, Norman Luhn, Primo
18416522281203 · 233222 + 5, d = 0, 6 10015 2020 Peter Kaiser, Primo
18416522281203 · 233222 - 1, d = 0, 6 10015 2020 Peter Kaiser, Primo

The Largest Known Gap between two proven primes

PrimesDigitsGap YearDiscoverer(s)
587 · 43103# / 11# - 455704 18662 1113106 2013 Michiel Jansen, Pierre Cami, Jens K. Andersen, Primo