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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: 10/7/06
Re: A conjecture for sets of four primes
Posted: Oct 11, 2013 6:22 PM
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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.

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