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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.
Only proved primes are allowed.

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