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".

Ranges of p (p|Mq or p|Rn)
0 < p < 1,000,000	1,000,000 < 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
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)