The number of ways of writing an integer n as a sum of two primes can be calculated explicitly as Length[Select[n - Table[Prime[i], {i, PrimePi[n]}], PrimeQ]] . … Hardy and John Littlewood in 1922 to be proportional to 2n Apply[Times, Map[(# - 1)/(# - 2)&, Map[First, Rest[FactorInteger[n]]]]]/Log[n] 2 It was proved in 1937 by Ivan Vinogradov that any large odd integer can be expressed as a sum of three primes.