double Mersenne number

A double Mersenne number is a number of the form 22p-1-1. Put another way, negative one plus 2 raised to the power of a Mersenne number. The first few double Mersenne numbers (and the ones small enough to show here) are: 3, 7, 127, 170141183460469231731687303715884105727.

If a double Mersenne number is itself prime, then it is called a double Mersenne prime. Obviously its index is then a Mersenne prime. The four double Mersenne numbers listed above are all primes, but as of today, 2170141183460469231731687303715884105727-1 is a probable primeMathworldPlanetmath, despite an intense effort to find factors. (According to the Prime Pages, if it’s composite, its least prime factorMathworldPlanetmath must be at least 5×1051.

Title double Mersenne number
Canonical name DoubleMersenneNumber
Date of creation 2013-03-22 17:38:50
Last modified on 2013-03-22 17:38:50
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A41