# [extropy-chat] 44th mersenne prime verified

spike spike66 at comcast.net
Tue Sep 12 01:53:10 UTC 2006

```We just got word that the 44th known Mersenne prime has been verified today.

This time the lucky exponent was 32582657.

However, 2^32582657-1 contains "only" 9,808,358 decimal digits so the
\$100,000 EFF award for a 10 million digit prime is *still* up for grabs.

This is a mind-boggling cluster of Mersenne primes way up here close to, but
under, the 10 million digit mark.  Perhaps we will have a long dry spell
now, one that could go on for years, after finding five record breakers in
under three years.  Perhaps we just don't understand something fundamental
somehow are distributed more densely as exponents get large?  How could that
possibly be?  No way.

In any case, here is a list of the 44 known Mersenne primes, where the
second column is the exponent in the form 2^n-1:

1	2   	2^2 -1 = 3, prime
2	3	2^3 -1 = 7, prime
3	5	2^5 -1 = 31, prime
4	7	2^7 -1 = 127, prime
5	13	2^13 -1 = 8191, prime
6	17	2^17 -1 = 131071, prime
7	19	2^19 -1 = 524287, prime
8	31	2^31 -1 = 2147483647, prime etc
9	61	(18 digit number)
10	89
11	107
12	127
13	521
14	607
15	1279
16	2203
17	2281
18	3217
19	4253
20	4423
21	9689
22	9941
23	11213
24	19937
25	21701
26	23209
27	44497
28	86243
29	110503
30	132049
31	216091
32	756839
33	859433
34	1257787
35	1398269
36	2976221
37	3021377
38	6972593
39	13466917
40	20996011
41	24036583
42	25964951
43	30402457
44	32582657

```