The Complexity of Goldbach's Conjecture
Description
The Goldbach's conjecture has been described as the most difficult problem in the history of Mathematics. This conjecture states that every even integer greater than 2 can be written as the sum of two primes. The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A major complexity classes are P and NSPACE(S(n)) for some S(n). We prove if the complexity class P is equal to NSPACE(S(n)) for some S(n) = o(log n), then the weak Goldbach's conjecture is false. Since Harald Helfgott proved that the weak Goldbach's conjecture is true, then we obtain that P is not equal to NSPACE(S(n)) for all S(n) = o(log n).
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