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- J. Richstein, "Verifying the goldbach conjecture up to 4· 1014," Math. Comp., 70:236 (2001) 1745--1749. MR 2002c:11131
Using a carefully optimized segmented sieve and an efficient checking algorithm, the Goldbach conjecture has been verified and is now known to be true up to 4· 1014. The program was distributed to various workstations. It kept track of maximal values of the smaller prime p in the minimal partition of the even numbers, where a minimal partition is a representation 2n = p + q with 2n - p' being composite for all p' < p. The maximal prime p needed in the considered interval was found to be 5569 and is needed for the partition 389965026819938 = 5569 + 389965026814369.