Mersenne Primes

A Mersenne number is a number that can be written as

$M_{p}=2^{p}-1$

where p is prime.

A Mersenne prime is a Mersenne number that is prime.

As an example, $2^{5}-1=31$ is a Mersenne prime, but $2^{11}-1=2047=23\times 89$ is a Mersenne number only.

There are 39 known Mersenne Primes:

Number	p	Number of digits in Mp
1	2	1
2	3	1
3	5	2
4	7	3
5	13	4
6	17	6
7	19	6
8	31	10
9	61	19
10	89	27
11	107	33
12	127	39
13	521	157
14	607	183
15	1279	386
16	2203	664
17	2281	687
18	3217	969
19	4253	1281
20	4423	1332
21	9689	2917
22	9941	2993
23	11213	3376
24	19937	6002
25	21701	6533
26	23209	6987
27	44497	13395
28	86243	25962
29	110503	33265
30	132049	39751
31	216091	65050
32	756839	227832
33	859433	258716
34	1257787	378632
35	1398269	420921
36	2976221	895932
37	3021377	909526
38	6972593	2098960
39	13466917	4053946