On Sunday, October 13, 2013 5:44:21 PM UTC+1, Ludovicus wrote:
> The condition of the even to be an square it is because to be even is not sufficient. For example 34 can be partitioned in four primes in 23 different forms, but the sum of its squares is not another square.
Since the condition of being a square isn't sufficient either (for example 36 = 6^2), that restriction is rather daft. Consider my revised Goldbach Conjecture: Every square of a positive even integer is the sum of two primes. It gets around the problem that 2 is not the sum of two primes, but that's rather daft, isn't it?