{"id":"palomar/PALOMAR-2026-11-02-000012","url":"https://github.com/sthubbar/goldbach-lean/tree/39d1ce6db8b634233ed29c2aa3e3dcf1218400dc/entries/saouter1998","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-02-000012-v1.json","repo":"https://github.com/sthubbar/goldbach-lean","tags":["math.NT","msc:11P32","msc:11Y11","msc:11A51"],"score":0,"title":"Checking the odd Goldbach conjecture up to 10^20","trust":"high","domain":"math.NT","source":"palomar","authors":["Steve Hubbard"],"reviews":0,"subject":"math.NT","summary":"A Lean 4 formalization of the mathematics of Y. Saouter, Checking the odd Goldbach conjecture up to 10^20, Math. Comp. 67, 1998, 863 to 866. Proved with no hypothesis: Lemma 1, the paper's form of Theorem 5 of Brillhart, Lehmer and Selfridge 1975, for every even F; Theorem 1, the primality criterion for N = 2^22 R + 1 below 10^20 with R odd and any base a with a^((N-1)/2) = -1 modulo N; Lemma 2 by quadratic reciprocity; Theorem 2, the case of base 5; the primality of the 100 rungs of Table 1 and of the first and last primes printed in the paper. The printed ladder constant 1258213 is a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-02","reactions":{},"formalized":true,"formalizes":[{"title":"Checking the odd Goldbach conjecture up to 10^20","identifier":"doi:10.1090/S0025-5718-98-00928-4","relationship":"formalizes"},{"title":"Numerical verification of the ternary Goldbach conjecture up to 8.875·10^30","identifier":"arXiv:1305.3062","relationship":"adapts"}]}