A Mersenne number is a number of the form M_n congruent 2^n - 1, where n is an integer. The Mersenne numbers consist of all 1s in base-2, and are therefore binary repunits. The first few Mersenne numbers are 1, 3, 7, 15, 31, 63, 127, 255, ... (OEIS A000225), corresponding to 1_2, 11_2, 111_2, 1111_2, ... in binary. The Mersenne numbers are also the numbers obtained by setting x = 1 in a Fermat polynomial. They also correspond to Cunningham numbers C^-(2, n). The number of digits D in the Mersenne number M_n is D = ⌊log(2^n - 1) + 1⌋, where ⌊x⌋ is the floor function, which, for large n, gives D≈⌊n log2 + 1⌋≈⌊0.301029n + 1⌋ = ⌊0.301029n⌋ + 1.
Catalan-Mersenne number | Cullen number | Cunningham number | double Mersenne number | Eberhart's conjecture | Erdős-Borwein constant | Fermat number | Lucas-Lehmer test | Mersenne prime | perfect number | repunit | Riesel number | Sierpiński number of the second kind | Sophie Germain prime | superperfect number | wheat and chessboard problem | Wieferich prime | Woodall number | Zsigmondy theorem
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