On Friday, October 11, 2013 5:37:04 PM UTC+1, 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.
Starting with n = 2: 4 is not the sum of four primes.
n = 4: 16 can be written as the sum of four primes in three ways. In neither case is the sum of the squares of the primes itself another square.
n = 6: 36 can be written as the sum of four primes in 15 ways. Guess what: The sum of squares of the primes is never a square.