MArt
 

..short for math and art.
Here is how excited you should be about this post..
[url]https://www.youtube.com/watch?v=4a2ZQtvMhRg[/url]

This is the reason behind the post:
[url]http://www.concinnitasproject.org/portfolio/[/url]

Perhaps these could be used as a "Rorschach" test.

For anyone who hasn't seen it yet:
[URL="https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK"]Proofs from The Book[/URL]

[QUOTE=Nick;569340]For anyone who hasn't seen it yet:
[URL="https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK"]Proofs from The Book[/URL][/QUOTE]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.

[QUOTE=xilman;569364]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.[/QUOTE]
Yes, that's the 2nd one.
And the 3rd one uses Mersenne numbers (for prime p, a prime factor of \(M_p\) is greater than p).

[QUOTE=jwaltos;569332]..short for math and art.
Here is how excited you should be about this post..
[url]https://www.youtube.com/watch?v=4a2ZQtvMhRg[/url]
[/QUOTE]

Why do I only see a dog watching football and jumping off the couch?

[QUOTE=petrw1;569376]Why do I only see a dog watching football and jumping off the couch?[/QUOTE]

Only?

[QUOTE=Nick;569340]For anyone who hasn't seen it yet:
[URL="https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK"]Proofs from The Book[/URL][/QUOTE]
The 6th edition regarding the "Sums of two squares" can be followed up with:[url]https://en.wikipedia.org/wiki/Geometry_and_the_Imagination[/url] (p.32, 1990 translation);[url]https://mathoverflow.net/questions/31113/zagiers-one-sentence-proof-of-a-theorem-of-fermat;[/url];[url]https://www.cambridge.org/core/books/number-theory-in-the-spirit-of-liouville/51A0D57710C50412C1C535049FACCE33[/url].
There is more to this than meets the eye.