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 2021-01-15, 05:40 #1 jwaltos     Apr 2012 Brady 2×33×7 Posts MArt ..short for math and art. Here is how excited you should be about this post.. https://www.youtube.com/watch?v=4a2ZQtvMhRg This is the reason behind the post: http://www.concinnitasproject.org/portfolio/ Perhaps these could be used as a "Rorschach" test. Last fiddled with by jwaltos on 2021-01-15 at 05:41
 2021-01-15, 10:54 #2 Nick     Dec 2012 The Netherlands 7×239 Posts For anyone who hasn't seen it yet: Proofs from The Book
2021-01-15, 15:09   #3
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

2×32×593 Posts

Quote:
 Originally Posted by Nick 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.

2021-01-15, 15:37   #4
Nick

Dec 2012
The Netherlands

7×239 Posts

Quote:
 Originally Posted by xilman 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.
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).

2021-01-15, 16:32   #5
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

121916 Posts

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

2021-01-16, 05:52   #6
jwaltos

Apr 2012

2·33·7 Posts

Quote:
 Originally Posted by petrw1 Why do I only see a dog watching football and jumping off the couch?
Only?

2021-01-16, 06:05   #7
jwaltos

Apr 2012

2·33·7 Posts

Quote:
 Originally Posted by Nick For anyone who hasn't seen it yet: Proofs from The Book
The 6th edition regarding the "Sums of two squares" can be followed up with:https://en.wikipedia.org/wiki/Geomet...he_Imagination (p.32, 1990 translation);https://mathoverflow.net/questions/3...rem-of-fermat;;https://www.cambridge.org/core/books...C535049FACCE33.
There is more to this than meets the eye.

Last fiddled with by jwaltos on 2021-01-16 at 06:06