Thread: MArt
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Old 2021-01-15, 15:09   #3
xilman's Avatar
May 2003
Down not across

299616 Posts

Originally Posted by Nick View Post
For anyone who hasn't seen it yet:
Proofs from The Book
I've not see the book itself so can't tell whether one of the six proofs of the infinitude of primes is the very elegant one based on the factorization of Mersenne numbers and Fermat numbers.

The basic idea is that F_n - 2 = 2^2^n - 1 = (2^2^(n-1) +1) (2^2^(n-1) -1) = F_{n-1} * (F_{n-1} -2)

by the difference of squares factorization formula and noting that F_n is co-prime to F_m when m != m.
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