Is there any chance that a seriously interested (but still home based) person can use MMA to check the latest claimed, largest Mersenne prime? My machine just overheats?
No. That number is enormous.
I mean you could. But it would be very difficult.
If I remember reading the article about it, it took them nearly a month of computing time on a grid of reasonably powerful machines to check.
Yes you can,
num = 2^74207281 - 1;
Do[If[Mod[num, n] == 0, Print["Fail"]; Abort[]], {n, 2,
Ceiling[Sqrt[num]], 2}];
leave that running for a while 
If you see a Fail, then it is not a primeā¦
In all seriousness, there are better (faster) ways of checking it. The above code takes forever. Have a look at this video:
https://www.youtube.com/watch?v=lEvXcTYqtKU
they explain a more reasonable way of checkingā¦ but still this takes a LONG time!!
Sean, Sander,
Many thanks for the helpful feedback. I will certainly take a look at the video.
Cheers,
David