Mersenne Mosts

Euclid knew that M7 was prime. It wasn't until 1461 that M13 was shown to be prime. Of course, they weren't called Mersenne primes in those days.
I wrote this from memory. Corrections welcomed.

One day in 1961, an IBM 7090 at UCLA was left to run the Lucas-Lehmer test overnight. The next day, Alex Hurwitz read the printouts and saw that M4253 was the 19th Mersenne prime. Success! A new world record! Alex finally calmed down and read the rest of the listing only to see that M4423 was also prime. Another world record! M4253 was King of the Mountain for less than 15 minutes.

19 hours on a Cray-2 in 1992.

11 minutes on the NEC SX-2 in January of 1988.

521 is over 4 times 127. The unfortunate Horace Scudder Uhler spent years looking for Mersenne primes in that range. He used mechanical calculators (and probably indentured grad students). He was not on speaking terms with D.H. Lehmer towards the end of his life.

M44497, M86243, M132049, M216091, M756839, M859433

M521, M607, M1279, M2203, and M2281

2^2-1, 2^(2^2-1)-1, 2^(2^(2^2-1)-1, ..., ?
= M2, M7, M127, 2^M127-1 ?
Thanks to Alex Hurwitz.