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M52
M52 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 52 (Provisional ranking) |
n-value : | 136,279,841 |
Number : | 881694327503...219486871551 |
Digits : | 41,024,320 |
Perfect number : | 2^{136,279,840} • (2^{136,279,841}-1) |
Digits : | 82,048,640 |
Discovery data : | |
Date of Discovery : | 2024-10-12 |
Discoverer : | Luke Durant |
Found with : | Fermat PRP test using PRPLL on NVIDIA A100 Lucas-Lehmer test using PRPLL on NVIDIA H100 |
Credits : | Mihai Preda George Woltman Aaron Blosser et. al. (PRPLL/GpuOwL, GIMPS & PrimeNet) |
M52 normally refers to the 52nd 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^{136,279,841}-1 was 2024-10-12 and has 41,024,320 digits.
A cloud-based network of machines volunteered by Luke Durant made the find on 2024-10-11.
This was the first Mersenne prime to be discovered by a GPU, the first since the founding of GIMPS not to be found by Prime95, and the first in the GIMPS era to originally be discovered as a probable prime rather than a LL-proven prime.
The official credit for the discovery goes to "L. Durant, M. Preda, 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:
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