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

Abstract

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).

2000 AMS Subject Classification:

• Primary 11P32
• Secondary 11A41
• 11Y11

Keywords:

• ternary Goldbach conjecture
• primality tests

Acknowledgments

We would like to thank the staff of the Direction des Systèmes d’Information at Université Paris VI/VII (Pierre et Marie Curie) and Bill Hart, at Warwick University, for allowing us to use their computer systems for this project. We would also like to thank Andrew Booker for suggesting that we exploit Proth primes. Travel was funded in part by the Leverhulme Prize.

Notes

¹Saouter exploited numbers of the form N=2²²·R+1 with N<10²⁰, , and R odd.

²In fact, the numbers returned by precprime were always prime.

³For comparison, Saouter sieved with the first 10 primes.