Does there exist more than 51 Mersenne primes below 2^136279841-1?
Basic
2
Ṁ206
2031
10%
chance

Alternatively, will GIMPS "double checks" reveal a previously unknown Mersenne prime?

LL tests, the main Mersenne primality proof test, requires two separate computers to produce the same "residue" to prove the primality of an "exponent". Now, probable prime tests are mostly used instead, which allows for a much lower cost verification, so the amount of computing power required is roughly halved per exponent. However, there still exists a large backlog of single LL tests that need to be double checked (with one goal of the project being completing them all by 2030).

The progress of this effort can be roughly viewed by checking the sum of the "available DC" column on this page: https://www.mersenne.org/primenet/

There can be a "residue mismatch" due to any number of factors, the main one being faulty computers producing erroneous results, so each unchecked single LL test could be hiding a Mersenne prime underneath.

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