Double Mersenne number information

In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p is prime...

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some...

The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by Makoto Matsumoto [ja] (松本 眞) and Takuji Nishimura...

fourth prime number, is not only a Mersenne prime (since 23 − 1 = 7) but also a double Mersenne prime since the exponent, 3, is itself a Mersenne prime. It...

Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers...

{\displaystyle 2^{p}-1} are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers. For...

numbers of special forms, such as Mersenne numbers. As of December 2018[update] the largest known prime number is a Mersenne prime with 24,862,048 decimal...

number and fifth super-prime. This is the prime index of the third Mersenne prime and second double Mersenne prime 127, as well as the third double Mersenne...

Smith number Double Mersenne number Zeisel number Heteromecic number Niven numbers Superparticular number Highly composite number Highly totient number Practical...

client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...

is a Mersenne prime. No odd perfect numbers are known; hence, all known perfect numbers are triangular. For example, the third triangular number is (3...

2^{n},\ldots ,2^{\infty }} values before chaos ensues. Two is the first Mersenne prime exponent, and it is the difference between the first two Fermat primes...

10-happy number. Paul Jobling discovered the prime in 2005. As of 2010[update], the largest known 10-happy prime is 242643801 − 1 (a Mersenne prime).[dubious...

computation of a double-width product and an explicit reduction step. If a modulus just less than a power of 2 is used (the Mersenne primes 231 − 1 and...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

e, 2.71828... 3 is the first Mersenne prime, as well as the second Mersenne prime exponent and the second double Mersenne prime exponent, for 7 and 127...

in the OEIS) The Fermat primes and the Mersenne primes form a subset of the binary palindromic primes. Any number n {\displaystyle n} is palindromic in...

numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47...

In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...

Woodall number W2m may be prime only if 2m + m is prime. As of January 2019, the only known primes that are both Woodall primes and Mersenne primes are...