Quote:
Originally Posted by drkirkby
This is my attempt to change the title. Putting no text whatsoever resulted in an error about the message being too short.

I think the edit would need to have been done
a) to the title of the first post in the thread, which is what names the thread;
b) within the time limit from posting that, which is one hour for us mere mortal nonmoderators (outside of personal blogs where we are in effect moderator). Occasionally if I start an edit before the hour is up, and finish it after an hour has passed since first posting, it still goes through. But the next attempt to edit the same post does not.
Looks like a moderator handled it for you in this thread (guessing Uncwilly).
Now to thread subject matter.
Yes a 2.6:1 asymmetry is intriguing. The sample sets are necessarily terribly small.
I'm surprised that fully a third of known Mersenne prime numbers' exponents are twin primes. That seems likely to decline as more Mersenne primes are found.
https://en.wikipedia.org/wiki/Twin_prime
So for twins, both of which are exponents of Mersenne primes, we have
3 5; 5 7; 17 19. I'm guessing we'll find no more such cases.
Dividing the list of exponents of Mersenne primes about in half and considering twins in each "half",
3 5 7 13 17 19 31 61 107 521 1279 4423 of Mp#1 to #25, 12 out of 25, 48% for the lower part
110503 132049 20996011 24036583 74207281 of Mp#26 to #51, 5 out of 26, 19.2% for the higher part.
For some other statistics related to Mersennne Prime exponents see
this.