M50
M50 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 50 (Provisional ranking) |
n-value : | 77,232,917 |
Number : | 467333183359...069762179071 |
Digits : | 23,249,425 |
Perfect number : | 2^{77,232,916} • (2^{77,232,917}-1) |
Digits : | 46,498,850 |
Discovery data : | |
Date of Discovery : | 2017-12-26 |
Discoverer : | Jonathan Pace |
Found with : | Lucas-Lehmer test Prime95 on Intel i5-6600 @ 3.30GHz |
Credits : | George Woltman Scott Kurowski Aaron Blosser (GIMPS & PrimeNet) |
M50 normally refers to the 50th Mersenne prime, in order of size from the smallest to greatest. This is the primary usage and what is referred to in the rest of this article. For clarification about other possible usages refer to the nomenclature and notation article.
Discovery
The official discovery date for prime 2^{77 232 917}-1 was 2017-12-26. See the press release for the full description of this discovery.
The discovery was made on a computer volunteered by Jonathan Pace using Prime95 (version 28.9). The machine was running on an Intel i5-6600 CPU at 3.30GHz.[1]. It was one of the minister's computers in a church, where Jonathan Pace serves as a deacon and a computer network administrator. [2] The primality proof took 6 days of non-stop computing.
The official credit for the discovery goes to "J. Pace, G. Woltman, S. Kurowski, A. Blosser, et al."
Verification
To confirm that there were no errors in the hardware or software, the number had to be independently verified by running tests on various machines with different architecture and software.
The volunteers that ran these tests were:
- Aaron Blosser verified it using Prime95 on an Intel Xeon server in 1.5 days
- David Stanfill verified it using gpuOwL on an AMD RX Vega 64 GPU in 1.4 days
- Andreas Höglund verified the prime using CUDALucas running on NVidia Titan Black GPU in 3.0 days
- Ernst Mayer verified it using his own program Mlucas on 32-core Xeon server in 3.4 days
- Andreas Höglund also confirmed using Mlucas running on an Amazon EC2 instance in 2.7 days