Quote:
Originally Posted by ET_
Playing with my applet, i found out this beautiful result:
M1000000000000000000000000000000000000000000000000000000001059 has a factor: 40000000000000000000000000000000000000000000000000000000042361
The factor being a 62digit prime (about 204.62 bit) obtained with trialfactoring software.
Geee, it's fun!
Luigi

If people would only learn a little mathematics, this kind of silliness would
stop. I keep telling people: do a little math BEFORE computing. But noone
seems to listen. I speculate that this is because math is hard, computing is easy, and participants herein can't be bothered doing anything that is *hard*.
The reward that comes from doing something HARD is a lot greater than
doing something EASY.
It is a *TOTALLY trivial* matter to find very large factors of very very large
Mersenne numbers. I will give a hint: Let p be a prime that is 3
mod 4 such that 2p+1 is also prime. Now consider the Mersenne
number M_p. Think 'quadratic reciprocity' and 'Euler's Theorem'.
Note that this 'factor' is discovered without any "trial division" at all.
What *would* be impressive would be finding a 62 digit factor of a
relatively small Mersenne number. (say) p < 2000.
And factors larger than 62 digits of Mersenne numbers have been found.
Quite a few. Look at 2^6831, 2^7271, and 2^8111, for example.