Goldbach's Even Number 122

Goldbach's Even Number 122. Let 2k₀ be the smallest even natural number ≥ 122 that cannot be expressed as the sum of two prime numbers. It follows that such a sum could not be expressed with fewer than four prime numbers. Proof : Since by hypothesis every prime number p less than 2k₀ differs from it by a composite number, (otherwise 2k₀ would be the sum of two primes), we can write : p + c = 2k₀ (c is composite). Since c is odd (p being odd), it is certainly the sum of an even number and an odd prime q : p + 2h + q = 2k₀. Now 2k₀ is by hypothesis the smallest value that cannot be expressed as the sum of two primes, and therefore 2h which is certainly not zero and less than 2k₀, is certainly the sum of two primes p' and q'. Therefore : 2k₀ = p + p' + q' + q. ■