16 What are Mersenne Primes?

A000225 – OEIS

The prime numbers among the Mersenne numbers are called Mersenne primes.

Mersenne primes are rare: so far (December 2018) only 51 of them have been found.

NR.PNUMBER OF DIGITS FROM M(P)YEAREXPLORER
121
231
352
473
51341456
61761555Johann Scheubel
71961555Johann Scheubel
831101772Leonhard Euler
961191883Iwan Perwuschin
1089271911Ralph E. Powers
11107331914Powers
12127391876Édouard Lucas
135211571952Raphael Robinson
146071831952Raphael Robinson
1512793861952Raphael Robinson
1622036641952Raphael Robinson
1722816871952Raphael Robinson
1832179691957Hans Riesel
19425312811961Alexander Hurwitz
20442313321961Alexander Hurwitz
21968929171963Donald B. Gillies
22994129931963Donald B. Gillies
2311.21333761963Donald B. Gillies
2419.93760021971Bryant Tuckerman
2521.70165331978Landon Curt Noll, Laura Nickel
2623.20969871979Landon CurtNoll
2744.49713.3951979David Slowinski, Harry L. Nelson
2886.24325.9621982David Slowinski
29110.50333.2651988Walter Colquitt, Luther Welsh Jr.
30132.04939.7511983David Slowinski
31216.09165.0501985David Slowinski
32756.839227.8321992David Slowinski, Paul Gage
33859.433258.7161994David Slowinski, Paul Gage
341.257.787378.6321996David Slowinski, Paul Gage
351.398.269420.9211996GIMPS/Joel Armengaud
362.976.221895.9321997GIMPS/Gordon Spence
373.021.377909.5261998GIMPS/Roland Clarkson
386.972.5932.098.9601999GIMPS/Nayan Hajratwala
3913.466.9174.053.9462001GIMPS/Michael Cameron
4020.996.0116.320.4302003GIMPS/Michael Shafer
4124.036.5837.235.7332004GIMPS/Josh Findley
4225.964.9517.816.2302005GIMPS/Martin Nowak
4330.402.4579.152.0522005GIMPS/Curtis Cooper, Steven Boone
4432.582.6579.808.3582006GIMPS/Curtis Cooper, Steven Boone
4537.156.66711.185.2722008GIMPS/Hans-Michael Elvenich
4642.643.80112.837.0642009GIMPS/Odd M. Strindmo
4743.112.60912.978.1892008GIMPS/Edson Smith
48?57.885.16117.425.1702013GIMPS/Curtis Cooper
49?74.207.28122.338.6182016GIMPS/Curtis Cooper
50?77.232.91723.249.4252017GIMPS/Jonathan Pace
51?82.589.93324.862.0482018GIMPS/Patrick Laroche

As of March 13, 2020, however, it cannot be ruled out that there are other, as yet undiscovered Mersenne primes between n = 43,112,609 and n = 82,589,933; therefore, the numbering from No. 48 onward is still uncertain (and marked with a “?”).