hermann on Sat, 16 Nov 2024 20:51:33 +0100


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Re: PARI/GP timings for operations on biggest known 41,024,320 decimal digit prime


On 2024-11-16 18:13, G. M.-S. wrote:

First, for me M_n is the n-th Mersenne prime, and not 2^n-1.

Well, presently nobody knows if 2^136279841-1 is the 52nd Mersenne
prime…

You are right, but we know that 2^136279841-1 is a Mersenne prime.

All Mersenne primes are known up to M_48.
The next four have a question mark because lower Mersenne
prime might exist:

https://t5k.org/primes/lists/all.txt

...
 rank  description                     digits   who   year comment
----- ------------------------------- -------- ----- ---- --------------
    1b 2^136279841-1                   41024320 MP1   2024 Mersenne 52??
    2  2^82589933-1                    24862048 G16   2018 Mersenne 51??
    3  2^77232917-1                    23249425 G15   2018 Mersenne 50??
    4  2^74207281-1                    22338618 G14   2016 Mersenne 49??
    5  2^57885161-1                    17425170 G13   2013 Mersenne 48
    6  2^43112609-1                    12978189 G10   2008 Mersenne 47
...

I asked and chances seem to be very low that 2^136279841-1 is not 52nd Mersenne prime:

https://www.mersenneforum.org/node/1060723#post1060782


Regards,

Hermann.