Verifying the Goldbach conjecture up to 4⋅10¹⁴

Richstein, Jörg

doi:10.1090/S0025-5718-00-01290-4

Verifying the Goldbach conjecture up to $4\cdot 10^{14}$
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by Jörg Richstein;

Math. Comp. 70 (2001), 1745-1749

DOI: https://doi.org/10.1090/S0025-5718-00-01290-4

Published electronically: July 18, 2000

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Abstract:

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 $4\cdot 10^{14}$. 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.

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