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.