Largest Known Primes

View the list of the largest known primes (mostly Mersenne Primes).

Mersenne Primes

Here is a list of all known Mersenne Primes. Also, the University of Tennessee Martin (utm.edu) maintains an outstanding Mersenne Primes page, courtesy of Chris Caldwell, including Mersenne Primes: History, Theorems and Lists.

Factors of Mersenne Numbers

I maintain a comprehensive list of factors of Mersenne numbers and Mersenne composites, through some N (which continues to grow).
The links below give lists of the smallest Mersenne number or Mersenne composite
Mq = 2^q - 1, each p divides, in the form

p | Mq    or   p | Rn,

where "p" is the (base 10) prime factor [1 or 7 (mod 8)], and "Mq" gives the prime power of the Mersenne number, or "Rn" gives the composite power of the Mersenne number. The vertical bar is used in the normal mathematical sense to mean "divides".

Ordered q (where p|Mq, written here as "q < p") over range 0 < p < 20,000,000,000
0 < q < 100,000	0 < q < 1,000,000
0 < q < 10,000,000	0 < q < 100,000,000
0 < q < 1,000,000,000	0 < q < 10,000,000,000
Ranges of p (p|Mq or p|Rn)
0 < p < 2,000,000	2,000,000 < p < 10,000,000
10,000,000 < p < 20,000,000	20,000,000 < p < 100,000,000
100,000,000 < p < 200,000,000	200,000,000 < p < 1,000,000,000
1,000,000,000 < p < 2,000,000,000	2,000,000,000 < p < 10,000,000,000
10,000,000,000 < p < 20,000,000,000
Ranges of p (p|Mq)
0 < p < 1,000,000,000 (M)	1,000,000,000 < p < 2,000,000,000 (M)
2,000,000,000 < p < 3,000,000,000 (M)	3,000,000,000 < p < 4,000,000,000 (M)
4,000,000,000 < p < 5,000,000,000 (M)	5,000,000,000 < p < 6,000,000,000 (M)
6,000,000,000 < p < 7,000,000,000 (M)	7,000,000,000 < p < 8,000,000,000 (M)
8,000,000,000 < p < 9,000,000,000 (M)	9,000,000,000 < p < 10,000,000,000 (M)
10,000,000,000 < p < 11,000,000,000 (M)	11,000,000,000 < p < 12,000,000,000 (M)
12,000,000,000 < p < 13,000,000,000 (M)	13,000,000,000 < p < 14,000,000,000 (M)
14,000,000,000 < p < 15,000,000,000 (M)	15,000,000,000 < p < 16,000,000,000 (M)
16,000,000,000 < p < 17,000,000,000 (M)	17,000,000,000 < p < 18,000,000,000 (M)
18,000,000,000 < p < 19,000,000,000 (M)	19,000,000,000 < p < 20,000,000,000 (M)
20,000,000,000 < p < 21,000,000,000 (M)	21,000,000,000 < p < 22,000,000,000 (M)
22,000,000,000 < p < 23,000,000,000 (M)	23,000,000,000 < p < 24,000,000,000 (M)
24,000,000,000 < p < 25,000,000,000 (M)	25,000,000,000 < p < 26,000,000,000 (M)
26,000,000,000 < p < 27,000,000,000 (M)	27,000,000,000 < p < 28,000,000,000 (M)
28,000,000,000 < p < 29,000,000,000 (M)	29,000,000,000 < p < 30,000,000,000 (M)
30,000,000,000 < p < 31,000,000,000 (M)	31,000,000,000 < p < 32,000,000,000 (M)
32,000,000,000 < p < 33,000,000,000 (M)	33,000,000,000 < p < 34,000,000,000 (M)
34,000,000,000 < p < 35,000,000,000 (M)	36,000,000,000 < p < 37,000,000,000 (M)
37,000,000,000 < p < 38,000,000,000 (M)	38,000,000,000 < p < 39,000,000,000 (M)
39,000,000,000 < p < 40,000,000,000 (M)	40,000,000,000 < p < 41,000,000,000 (M)
41,000,000,000 < p < 42,000,000,000 (M)	42,000,000,000 < p < 43,000,000,000 (M)
43,000,000,000 < p < 44,000,000,000 (M)	44,000,000,000 < p < 45,000,000,000 (M)
45,000,000,000 < p < 46,000,000,000 (M)	46,000,000,000 < p < 47,000,000,000 (M)
47,000,000,000 < p < 48,000,000,000 (M)	80,000,000,000 < p < 81,000,000,000 (M)
81,000,000,000 < p < 82,000,000,000 (M)	82,000,000,000 < p < 83,000,000,000 (M)
Mersenne Palindromes
Factors p are [1 or 7 (mod 8)]
Palindrome primes p, q such that (p|Mq) [palindrome factors of palindrome Mersenne numbers]
0 < p < 30,000,000,000
Palindrome prime p, palindrome n such that (p|Mn or p|Rn)
0 < p < 30,000,000,000
Palindrome prime p, integer n such that (p|Mn or p|Rn)
0 < p < 30,000,000,000
Prime p, palindrome prime q such that (p|Mq) [all factors of palindrome Mersenne numbers]
0 < p < 30,000,000,000
Prime p, palindrome n such that (p|Mn or p|Rn)
0 < p < 30,000,000,000

Mersenne Chains

Mersenne Chains are series of primes q0,q1,...,qn where every member of the series = 1 or 7 (mod 8), and for which each prime qx in the series divides 2^(q[x+1]) - 1. Note that the Mersenne number factor files above are the Mersenne chain lists of length 2, so we only address longer Mersenne chains in this section.

Mersenne chains, length 4 or greater
Mersenne chains, length 3 or greater [large file]