M51
M51 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 51* |
n-value : | 82,589,933 |
Number : | 148894445742...325217902591 |
Digits : | 24,862,048 |
Perfect number : | 2^{82,589,932} • (2^{82,589,933}-1) |
Digits : | 49,724,095 |
Discovery data : | |
Date of Discovery : | 2018-12-07 |
Discoverer : | Patrick Laroche |
M51 normally refers to the 51th 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.
Discovery
The official discovery date for prime 2^{82,589,933}-1 was 2018-12-21 and has 24,862,048 digits.
A computer volunteered by Patrick Laroche made the find on 2018-12-07. The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU.
The official credit for the discovery goes to "P. Laroche, G. Woltman, 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:
- Andreas Höglund verified the prime using CUDALucas running on a NVidia V100 GPU in 21 hours.
- Andreas Höglund also verified the prime using Mlucas running on 16 cores of an Amazon AWS instance in 72 hours.
- Aaron Blosser also verified it using Prime95 on an Intel 7700K processor in 6 days, 8 hours.