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Topic: A conjecture for sets of four primes
Replies: 12   Last Post: Oct 14, 2013 8:11 PM

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Registered: 2/12/07
Re: A conjecture for sets of four primes
Posted: Oct 11, 2013 1:02 PM
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On Friday, October 11, 2013 12:37:04 PM UTC-4, Ludovicus wrote:
> "Any square of an even number can be decomposed as the sums of 4 prime numbers. The sum of the squares of one of the sets is another square." The first part is based in Goldbach's Conjecture. The second I suppose is a new conjecture.

The conjecture as stated is trivially false. 4 is not the sum of 4 prime
numbers. OTOH, any integer >5 is the sum of 3 primes by Helfgott's
recent result (Ternary Goldbach), so it is easy to see that ANY integer >7
is the sum of 4 primes by Goldbach's Binary Conjecture.

"square of an even number" is a red herring.

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