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What are Mersenne numbers?


Are integers of the form MP= 2P -1.

If MP is a prime number, the number P It is also. They are named after their most distinguished scholar, Marin Mersenne. The first ones are the null mersenne (M0 = 0) and the unit (M1 = 1). There are prime and non-prime mersennes, but cousins ​​are the most studied.

There are currently 49 Mersenne prime numbers known. The last one was discovered on January 7th, 2016. Check out the table below.

List of known Mersenne cousins

#2P-1DigitsYear
122-11500 A.C.
223-11500 A.C.
325-12275 A.C.
427-13275 A.C
5213-141456
6217-161588
7219-161588
8231-1101772
9261-1191883
10289-1271911
112107-1331914
122127-1391876
132521-11571952
142607-11831952
1521,279-13861952
1622,203-16641952
1722,281-16871952
1823,217-19691957
1924,253-11,2811961
2024,423-11,3321961
2129,689-12,9171963
2229,941-12,9931963
23211,213-13,3761963
24219,937-16,0021971
25221,701-16,5331978
26223,209-16,9871979
27244,497-113,3951979
28286,243-125,9621982
292110,503-133,2651988
302132,049-139,7511983
312216,091-165,0501985
322756,839-1227,8321992
332859,433-1258,7161994
3421,257,787-1378,6321996
3521,398,269-1420,9211996
3622,976,221-1895,9321997
3723,021,377-1909,5261998
3826,972,593-12,098,9601999
39213,466,917-14,053,9462001
40220,996,011-16,320,4302003
41224,036,583-17,235,7332004
42225,964,951-17,816,2302005
43230,402,457-19,152,0522005
44232,582,657-19,808,3582006
45237,156,667-111,185,2722008
46242,643,801-112,837,0642009
47243,112,609-112,978,1892008
48257,885,161-117,425,1702013
49274,207,281-122,338,6182016