My prime records

Prime records I have a share in (parentheses means it is no longer the record).

Largest k-tuplet for k = (3), (6), 7, 8, (9), 10, 11, (12), 13, (14), 15, (16)
Largest AP-k for k = (3), (5), (9), (10), (11), (12), (13), (14), (15), (16), (17), 18, (19)
Largest CPAP-k for k = (3), (4), 6, 7, 8, 9, and with prp's allowed for k = 3
Smallest CPAP-k for k = (7), 8, 9
Largest CPAP-k difference for k = 3, (4), (5), 6, 7
Largest CC-k of the 1st kind for k = (5), (6), (7), (8), (9), (10), 11, 12, (13), 14, (15)
Largest CC-k of the 2nd kind for k = (5), (6), 7, (8), (9), (10), (11), (12), 13, 14, (15)
Largest BiTwin with k links for k = (2), (3), (4), (5), 6, (7) (k links has 2k+2 primes)
Largest Generalized BiTwin with k links for k = 1, (2), 3, 4, 5, 6

The above include the largest overall case of k simultaneous primes for k = (6), (7), (8), (9), (10), 11, (12), 13, (14), (15), (16)

Largest probable primes gap and (largest proven prime gap)
Largest prime gap with merit at least m for m = 11.28, 30.04
Around 20000 other records for first known occurrence prime gaps

Various other records and special primes, e.g.:
Minimal AP-k with smallest possible difference (k#) for k = 15, 16, 17, 18
Largest k consecutive complete factorizations for k = (4), (5), (6), (7), and with prp's allowed for k = (3), (4)
Largest doubly palindromic prime
Largest reversible prime - also called emirp
Largest prime vampire number
(Largest prime partition number)
Largest semi-prime twins
Largest sexy prime (pair), triplet, quadruplet
Largest (cousin primes) and cousin prp's
Largest Ruth-Aaron pair
Prime with 101 titanic prime factors in p+1
Primes of form k*[RSA-200]^512-1, only provable with factorization of RSA-200.
Prime of form k*C(x,23)-1 with 6 non-constructed 3k factors in p+1
100000-digit picture prime with digits forming text
(Largest Chen prime)
Largest binomial prime of form C(x,6)+1
 Largest Cuban prime
(Largest proven Fibonacci cofactor)
Largest prp cofactor of a (Mersenne), repunit, Cullen, Woodall, (Fibonacci), (Lucas) number
Longest sequence of doubly consecutive primes
Largest weakly prime
Largest Honaker prime
A prime tree of depth 26

Most of the records were found with:
1) A sieve by me to eliminate candidates with small factors.
2) The GMP library or PrimeForm/GW for probable prime testing.
3) Tony Forbes' VFYPR, Marcel Martin's Primo, or PrimeForm/GW for primality proving.

I have cooperated with many people who are credited on the linked pages. I especially want to thank Torbjörn Alm and Hans Rosenthal for finding lots of records using my programs.

Many contributions to Carlos Rivera's The Prime Puzzles & Problems Connection (search on Andersen) involve results not listed here.

I would like to hear about improvements of listed records without parentheses.
Maintained by Jens Kruse Andersen, jens.k.a@get2net.dk   home
Last updated 18 December 2011.