Admin: Created page with "{{ConstantsFlag}} 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...."

2019-03-16T06:48:46Z

Created page with "{{ConstantsFlag}} A Mersenne number is a number that can be written as <math> M_p = 2^p - 1 </math> where p is prime. A Mersenne prime is a Mersenne number that is prime...."

New page

{{ConstantsFlag}}

A Mersenne number is a number that can be written as

<math>
M_p = 2^p - 1
</math>

where p is prime.

A Mersenne prime is a Mersenne number that is prime.

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

There are 39 known Mersenne Primes:

{|class="wikitable"
|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
|}

Mersenne Primes - Revision history

Admin: Created page with "{{ConstantsFlag}} 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...."

Admin: Created page with "{{ConstantsFlag}} 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...."