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M52

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M52
Prime class :
Type : Mersenne prime
Formula : Mn = 2n - 1
Prime data :
Rank : 52 (Provisional ranking)
n-value : 136,279,841
Number : 881694327503...219486871551
Digits : 41,024,320
Perfect number : 2136,279,840 • (2136,279,841-1)
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 2136,279,841-1 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:

Fill in.

External links