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.