Using a variation of the strikingly consistent methodology for guessing M51, to make predictions about M52:

Code:

ID Ballpark Basis of ballpark Guess exp Mod 8 Date guess
52a 88,318,521 ratio of previous two 88318673 1 Jun 14, 2019 Flag Day
52b 121,882,920 Approx expected ratio 1.47576*p51 121882753 1 May 21, 2025 Assuming 6 million/year first test range covered
52c 402,143,506 A long stride, 521/107*p51 402143633 1 Mar 12, 2052 " "

These have been tweaked to be 1 mod 8, since the probabilities are better there as I recall. Yes:

https://www.mersenneforum.org/showpo...2&postcount=53 by GP2.

They have fractions of interior ones bits averaging 0.468, near the trend for higher known Mersenne prime exponents (0.479 overall and declining).

The methodology for predicting M51 was 100% consistent in selecting exponents that did not produce M1, and at least 2 out of 3 did not predict prime numbers. (What's 40 years of hunting, beginning with a programmable calculator to play with the low end.)

I predict M52 will be none of these new guesses.

If I squint a bit, it looks a little like Murphy of Murphy's law making a certain hand gesture in GP2's right digit hexadecimal histogram.

But hey, we're in it for the fun and learning, not fame or fortune.