论文信息 - Numerical Verification of the Ternary Goldbach Conjecture up to 8.875·1030 - 字舞流文

Numerical Verification of the Ternary Goldbach Conjecture up to 8.875·1030

We describe a computation that confirms the ternary Goldbach conjecture up to 8 875 694 145 621 773 516 800 000 000 000 (>8.875·1030).

David J. Platt | H. A. Helfgott

[1] Gerhard Rosenberger,et al. Number Theory: An Introduction via the Distribution of Primes , 2006 .

[2] H. Helfgott. Major arcs for Goldbach's problem , 2013, 1305.2897.

[3] François Morain,et al. Easy numbers for the elliptic curve primality proving algorithm , 1992, ISSAC '92.

[4] David J. Platt,et al. Computing degree-1 L-functions rigorously , 2011 .

[5] Yannick Saouter,et al. Short effective intervals containing primes , 2003 .

[6] Matti K. Sinisalo. Checking the Goldbach conjecture up to 4⋅10¹¹ , 1993 .

[7] H. Helfgott. Minor arcs for Goldbach's problem , 2012, 1205.5252.

[8] Karim Belabas,et al. User’s Guide to PARI / GP , 2000 .

[9] Tommy Färnqvist. Number Theory Meets Cache Locality – Efficient Implementation of a Small Prime FFT for the GNU Multiple Precision Arithmetic Library , 2005 .

[10] Siegfried Herzog,et al. Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018 , 2013, Math. Comput..

[11] Xavier. The 10 13 first zeros of the Riemann Zeta function , and zeros computation at very large height , 2004 .

[12] Yannick Saouter,et al. Checking the odd Goldbach conjecture up to 1020 , 1998, Math. Comput..