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Numerical results on the Goldbach conjecture

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Abstract

The number of Goldbach partitions has been computed for all even numbers ≦ 350,000 and compared to well-known theoretical estimates. The random fluctuations are slowly decreasing and less than ± 5 per cent at the upper end of the interval. The number of partitions is given explicitly for 2n,n=3(1)22. Further, if for a givenN the smallest prime in all partitions of 2N isa=a(2N) we have also determineda 1(2N 1)<a 2(2N 2)<... withN 1<N 2<... such thatn<N k impliesa(2n)<a k (2N k ) up to 2n=40,000,000.

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References

  1. Mok-Kong Shen,On Checking the Goldbach Conjecture, BIT 4 (1964), 243–245.

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  1. Department of Computer Sciences, Lund University, Sölvegatan 14 A, S-22362, Lund, Sweden

    Jan Bohman & Carl-Erik Fröberg

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  1. Jan Bohman
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  2. Carl-Erik Fröberg
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Bohman, J., Fröberg, CE. Numerical results on the Goldbach conjecture. BIT 15, 239–243 (1975). https://doi.org/10.1007/BF01933655

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  • DOI: https://doi.org/10.1007/BF01933655

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