Verification logs for: Extending the Verified Range for A!B!=C! to B <= 10^1,000,000,000 Test system: Apple M1 Max, 10 cores, 64 GB, macOS (darwin/arm64), Go 1.26.0 Current downloads (SHA-256, complete files): factorial_solver.go 80a6abf56ec92c1b4c3b8d06ea171840b28a880fb1a9a8ce597dac7e62f71168 factorial_solver_hybrid.go 5a110d4547ce8bffde944b6d0fe5e3987f282bb09c1c65ae12645850dba0a557 (revision 2) Source bodies used for the recorded runs (SHA-256, beginning at //go:build ignore): factorial_solver.go a8814c1d9b146550871349ea1b6fa555537c194d4ea8d5b75b07d6aaabb4d216 (section 1) factorial_solver_hybrid.go 3f196533a42bacf36093e955090ac1fb34a2391b98213a0ed183891913b1efcd (sections 3-6) The current downloads prepend six comment lines of publication-license metadata; their source bodies are byte-for-byte identical to the recorded bodies above. The superseded revision 1 source used in section 2 is identified by SHA-256 3a8cd9157981ddf0d6cfbd0a73ff4a1db51706ef2b942142ffbdfe92ee405549 but is not included in this archive. Compiled binaries from the recorded runs are not archived. ====================================================================== 1. Lower-range reproduction, 10^6 <= B <= 10^3000 (factorial_solver.go) ====================================================================== searching hypothetical solutions other than (6,7,10) B range : 10^6 .. 10^3000 bounds : A <= 9994, 2 <= k=C-B <= 14 workers : 10 known nontrivial solution: 6! * 7! = 10! new solutions found : 0 (A,k) pairs examined : 87408 reduced kth roots : 47248 full-root fallbacks : 0 exact product compares : 310161 elapsed : 8.9863595s ====================================================================== 2. Hybrid revision 1, D=10^6, full survivor trajectory ====================================================================== searching hypothetical solutions other than (6,7,10) B range : 10^3000 .. 10^1000000 bounds : A <= 3321973, 2 <= k=C-B <= 23 workers : 10 filters : up to 64 exact prime-field filters hybrid : sparse polynomial-GCD mode at <= 5000 survivors memory : up to 1024 MiB extra for dense filter parallelism filter 1 q=3321977 [dense image x10] -> 24698907 surviving (A,k) pairs filter 2 q=3322091 [dense image x10] -> 13465532 surviving (A,k) pairs filter 3 q=3322213 [dense image x10] -> 7674010 surviving (A,k) pairs filter 4 q=3322337 [dense image x10] -> 4522454 surviving (A,k) pairs filter 5 q=3322439 [dense image x10] -> 2729113 surviving (A,k) pairs filter 6 q=3322547 [dense image x10] -> 1674509 surviving (A,k) pairs filter 7 q=3322679 [dense image x10] -> 1040179 surviving (A,k) pairs filter 8 q=3322783 [dense image x10] -> 650031 surviving (A,k) pairs filter 9 q=3322889 [dense image x10] -> 408328 surviving (A,k) pairs filter 10 q=3323003 [dense image x10] -> 257232 surviving (A,k) pairs filter 11 q=3323113 [dense image x10] -> 162260 surviving (A,k) pairs filter 12 q=3323213 [dense image x10] -> 102718 surviving (A,k) pairs filter 13 q=3323399 [dense image x10] -> 65180 surviving (A,k) pairs filter 14 q=3323543 [dense image x10] -> 41441 surviving (A,k) pairs filter 15 q=3323659 [dense image x10] -> 26330 surviving (A,k) pairs filter 16 q=3323783 [dense image x10] -> 16806 surviving (A,k) pairs filter 17 q=3323921 [dense image x10] -> 10645 surviving (A,k) pairs filter 18 q=3324047 [dense image x10] -> 6797 surviving (A,k) pairs filter 19 q=3324151 [dense image x10] -> 4309 surviving (A,k) pairs filter 20 q=3324257 [sparse gcd] -> 2748 surviving (A,k) pairs filter 21 q=3324359 [sparse gcd] -> 1707 surviving (A,k) pairs filter 22 q=3324467 [sparse gcd] -> 1081 surviving (A,k) pairs filter 23 q=3324569 [sparse gcd] -> 687 surviving (A,k) pairs filter 24 q=3324679 [sparse gcd] -> 463 surviving (A,k) pairs filter 25 q=3324779 [sparse gcd] -> 291 surviving (A,k) pairs filter 26 q=3324913 [sparse gcd] -> 193 surviving (A,k) pairs filter 27 q=3325027 [sparse gcd] -> 118 surviving (A,k) pairs filter 28 q=3325159 [sparse gcd] -> 71 surviving (A,k) pairs filter 29 q=3325261 [sparse gcd] -> 53 surviving (A,k) pairs filter 30 q=3325373 [sparse gcd] -> 31 surviving (A,k) pairs filter 31 q=3325519 [sparse gcd] -> 18 surviving (A,k) pairs filter 32 q=3325631 [sparse gcd] -> 6 surviving (A,k) pairs filter 33 q=3325733 [sparse gcd] -> 4 surviving (A,k) pairs filter 34 q=3325849 [sparse gcd] -> 4 surviving (A,k) pairs filter 35 q=3325957 [sparse gcd] -> 3 surviving (A,k) pairs filter 36 q=3326069 [sparse gcd] -> 2 surviving (A,k) pairs filter 37 q=3326171 [sparse gcd] -> 2 surviving (A,k) pairs filter 38 q=3326287 [sparse gcd] -> 1 surviving (A,k) pairs filter 39 q=3326399 [sparse gcd] -> 0 surviving (A,k) pairs size-bound candidates : 47698417 pairs filters actually used : 39 filter primes : [3321977 3322091 3322213 3322337 3322439 3322547 3322679 3322783] ... [3325631 3325733 3325849 3325957 3326069 3326171 3326287 3326399] filter build : 7.810024583s modular survivors : 0 pairs inside B-range : 0 pairs known nontrivial solution: 6! * 7! = 10! new solutions found : 0 (A,k) pairs examined : 0 reduced kth roots : 0 full-root fallbacks : 0 exact product compares : 0 elapsed : 7.834883625s ====================================================================== 3. Hybrid revision 2 (recorded source body above), D=10^6, full survivor trajectory ====================================================================== searching hypothetical solutions other than (6,7,10) B range : 10^3000 .. 10^1000000 bounds : A <= 3321973, 2 <= k=C-B <= 23 workers : 10 filters : up to 64 exact prime-field filters hybrid : sparse polynomial-GCD mode at <= 5000 survivors memory : dense image bitsets grouped within 8192 MiB filter 1 q=3321977 [dense image x10 g1] -> 24698907 surviving (A,k) pairs filter 2 q=3322091 [dense image x10 g1] -> 13465532 surviving (A,k) pairs filter 3 q=3322213 [dense image x10 g1] -> 7674010 surviving (A,k) pairs filter 4 q=3322337 [dense image x10 g1] -> 4522454 surviving (A,k) pairs filter 5 q=3322439 [dense image x10 g1] -> 2729113 surviving (A,k) pairs filter 6 q=3322547 [dense image x10 g1] -> 1674509 surviving (A,k) pairs filter 7 q=3322679 [dense image x10 g1] -> 1040179 surviving (A,k) pairs filter 8 q=3322783 [dense image x10 g1] -> 650031 surviving (A,k) pairs filter 9 q=3322889 [dense image x10 g1] -> 408328 surviving (A,k) pairs filter 10 q=3323003 [dense image x10 g1] -> 257232 surviving (A,k) pairs filter 11 q=3323113 [dense image x10 g1] -> 162260 surviving (A,k) pairs filter 12 q=3323213 [dense image x10 g1] -> 102718 surviving (A,k) pairs filter 13 q=3323399 [dense image x10 g1] -> 65180 surviving (A,k) pairs filter 14 q=3323543 [dense image x10 g1] -> 41441 surviving (A,k) pairs filter 15 q=3323659 [dense image x10 g1] -> 26330 surviving (A,k) pairs filter 16 q=3323783 [dense image x10 g1] -> 16806 surviving (A,k) pairs filter 17 q=3323921 [dense image x10 g1] -> 10645 surviving (A,k) pairs filter 18 q=3324047 [dense image x10 g1] -> 6797 surviving (A,k) pairs filter 19 q=3324151 [dense image x10 g1] -> 4309 surviving (A,k) pairs filter 20 q=3324257 [sparse gcd] -> 2748 surviving (A,k) pairs filter 21 q=3324359 [sparse gcd] -> 1707 surviving (A,k) pairs filter 22 q=3324467 [sparse gcd] -> 1081 surviving (A,k) pairs filter 23 q=3324569 [sparse gcd] -> 687 surviving (A,k) pairs filter 24 q=3324679 [sparse gcd] -> 463 surviving (A,k) pairs filter 25 q=3324779 [sparse gcd] -> 291 surviving (A,k) pairs filter 26 q=3324913 [sparse gcd] -> 193 surviving (A,k) pairs filter 27 q=3325027 [sparse gcd] -> 118 surviving (A,k) pairs filter 28 q=3325159 [sparse gcd] -> 71 surviving (A,k) pairs filter 29 q=3325261 [sparse gcd] -> 53 surviving (A,k) pairs filter 30 q=3325373 [sparse gcd] -> 31 surviving (A,k) pairs filter 31 q=3325519 [sparse gcd] -> 18 surviving (A,k) pairs filter 32 q=3325631 [sparse gcd] -> 6 surviving (A,k) pairs filter 33 q=3325733 [sparse gcd] -> 4 surviving (A,k) pairs filter 34 q=3325849 [sparse gcd] -> 4 surviving (A,k) pairs filter 35 q=3325957 [sparse gcd] -> 3 surviving (A,k) pairs filter 36 q=3326069 [sparse gcd] -> 2 surviving (A,k) pairs filter 37 q=3326171 [sparse gcd] -> 2 surviving (A,k) pairs filter 38 q=3326287 [sparse gcd] -> 1 surviving (A,k) pairs filter 39 q=3326399 [sparse gcd] -> 0 surviving (A,k) pairs size-bound candidates : 47698417 pairs filters actually used : 39 filter primes : [3321977 3322091 3322213 3322337 3322439 3322547 3322679 3322783] ... [3325631 3325733 3325849 3325957 3326069 3326171 3326287 3326399] filter build : 7.104885625s modular survivors : 0 pairs inside B-range : 0 pairs known nontrivial solution: 6! * 7! = 10! new solutions found : 0 (A,k) pairs examined : 0 reduced kth roots : 0 full-root fallbacks : 0 exact product compares : 0 elapsed : 7.104999041s ====================================================================== 4. Hybrid revision 2 (recorded source body above), D=10^7 ====================================================================== searching hypothetical solutions other than (6,7,10) B range : 10^3000 .. 10^10000000 bounds : A <= 33219332, 2 <= k=C-B <= 26 workers : 10 filters : up to 80 exact prime-field filters hybrid : sparse polynomial-GCD mode at <= 2000000 survivors memory : dense image bitsets grouped within 8192 MiB filter 1 q=33219341 [dense image x10 g1] -> 266819446 surviving (A,k) pairs filter 2 q=33219443 [dense image x10 g1] -> 143444814 surviving (A,k) pairs filter 3 q=33219559 [dense image x10 g1] -> 80760090 surviving (A,k) pairs filter 4 q=33219661 [dense image x10 g1] -> 47160410 surviving (A,k) pairs filter 5 q=33219803 [dense image x10 g1] -> 28292385 surviving (A,k) pairs filter 6 q=33219911 [dense image x10 g1] -> 17300741 surviving (A,k) pairs filter 7 q=33220013 [dense image x10 g1] -> 10706192 surviving (A,k) pairs filter 8 q=33220129 [dense image x10 g1] -> 6683339 surviving (A,k) pairs filter 9 q=33220237 [dense image x10 g1] -> 4192828 surviving (A,k) pairs filter 10 q=33220337 [dense image x10 g1] -> 2639365 surviving (A,k) pairs filter 11 q=33220459 [dense image x10 g1] -> 1664045 surviving (A,k) pairs filter 12 q=33220571 [sparse gcd] -> 1051245 surviving (A,k) pairs filter 13 q=33220673 [sparse gcd] -> 664667 surviving (A,k) pairs filter 14 q=33220793 [sparse gcd] -> 420781 surviving (A,k) pairs filter 15 q=33220909 [sparse gcd] -> 267088 surviving (A,k) pairs filter 16 q=33221011 [sparse gcd] -> 169403 surviving (A,k) pairs filter 17 q=33221137 [sparse gcd] -> 107504 surviving (A,k) pairs filter 18 q=33221249 [sparse gcd] -> 68168 surviving (A,k) pairs filter 19 q=33221369 [sparse gcd] -> 43281 surviving (A,k) pairs filter 20 q=33221479 [sparse gcd] -> 27474 surviving (A,k) pairs filter 21 q=33221579 [sparse gcd] -> 17402 surviving (A,k) pairs filter 22 q=33221693 [sparse gcd] -> 11012 surviving (A,k) pairs filter 23 q=33221807 [sparse gcd] -> 6892 surviving (A,k) pairs filter 24 q=33221957 [sparse gcd] -> 4393 surviving (A,k) pairs filter 25 q=33222061 [sparse gcd] -> 2753 surviving (A,k) pairs filter 26 q=33222179 [sparse gcd] -> 1745 surviving (A,k) pairs filter 27 q=33222283 [sparse gcd] -> 1099 surviving (A,k) pairs filter 28 q=33222383 [sparse gcd] -> 697 surviving (A,k) pairs filter 29 q=33222499 [sparse gcd] -> 443 surviving (A,k) pairs filter 30 q=33222601 [sparse gcd] -> 291 surviving (A,k) pairs filter 31 q=33222701 [sparse gcd] -> 177 surviving (A,k) pairs filter 32 q=33222809 [sparse gcd] -> 119 surviving (A,k) pairs filter 33 q=33222923 [sparse gcd] -> 71 surviving (A,k) pairs filter 34 q=33223027 [sparse gcd] -> 47 surviving (A,k) pairs filter 35 q=33223129 [sparse gcd] -> 31 surviving (A,k) pairs filter 36 q=33223261 [sparse gcd] -> 21 surviving (A,k) pairs filter 37 q=33223367 [sparse gcd] -> 15 surviving (A,k) pairs filter 38 q=33223507 [sparse gcd] -> 13 surviving (A,k) pairs filter 39 q=33223639 [sparse gcd] -> 9 surviving (A,k) pairs filter 40 q=33223741 [sparse gcd] -> 5 surviving (A,k) pairs filter 41 q=33223859 [sparse gcd] -> 3 surviving (A,k) pairs filter 42 q=33223961 [sparse gcd] -> 1 surviving (A,k) pairs filter 43 q=33224083 [sparse gcd] -> 1 surviving (A,k) pairs filter 44 q=33224207 [sparse gcd] -> 1 surviving (A,k) pairs filter 45 q=33224311 [sparse gcd] -> 1 surviving (A,k) pairs filter 46 q=33224413 [sparse gcd] -> 1 surviving (A,k) pairs filter 47 q=33224519 [sparse gcd] -> 1 surviving (A,k) pairs filter 48 q=33224623 [sparse gcd] -> 1 surviving (A,k) pairs filter 49 q=33224743 [sparse gcd] -> 0 surviving (A,k) pairs size-bound candidates : 523679824 pairs filters actually used : 49 filter primes : [33219341 33219443 33219559 33219661 33219803 33219911 33220013 33220129] ... [33223961 33224083 33224207 33224311 33224413 33224519 33224623 33224743] filter build : 2m31.650953167s modular survivors : 0 pairs inside B-range : 0 pairs known nontrivial solution: 6! * 7! = 10! new solutions found : 0 (A,k) pairs examined : 0 reduced kth roots : 0 full-root fallbacks : 0 exact product compares : 0 elapsed : 2m31.65106475s ====================================================================== 5. Hybrid revision 2 (recorded source body above), D=10^8 ====================================================================== searching hypothetical solutions other than (6,7,10) B range : 10^3000 .. 10^100000000 bounds : A <= 332192867, 2 <= k=C-B <= 29 workers : 10 filters : up to 80 exact prime-field filters hybrid : sparse polynomial-GCD mode at <= 2000000 survivors memory : dense image bitsets grouped within 16384 MiB filter 1 q=332192873 [dense image x10 g1] -> 2938135344 surviving (A,k) pairs filter 2 q=332192977 [dense image x10 g1] -> 1599382779 surviving (A,k) pairs filter 3 q=332193089 [dense image x10 g1] -> 909713114 surviving (A,k) pairs filter 4 q=332193203 [dense image x10 g1] -> 535286073 surviving (A,k) pairs filter 5 q=332193383 [dense image x10 g1] -> 322841490 surviving (A,k) pairs filter 6 q=332193529 [dense image x10 g1] -> 198016618 surviving (A,k) pairs filter 7 q=332193629 [dense image x10 g1] -> 122824537 surviving (A,k) pairs filter 8 q=332193751 [dense image x10 g1] -> 76756974 surviving (A,k) pairs filter 9 q=332193859 [dense image x10 g1] -> 48188036 surviving (A,k) pairs filter 10 q=332193989 [dense image x10 g1] -> 30348691 surviving (A,k) pairs filter 11 q=332194091 [dense image x10 g1] -> 19150153 surviving (A,k) pairs filter 12 q=332194193 [dense image x10 g1] -> 12098916 surviving (A,k) pairs filter 13 q=332194321 [dense image x10 g1] -> 7653338 surviving (A,k) pairs filter 14 q=332194487 [dense image x10 g1] -> 4842340 surviving (A,k) pairs filter 15 q=332194601 [dense image x10 g1] -> 3063836 surviving (A,k) pairs filter 16 q=332194703 [dense image x10 g1] -> 1938695 surviving (A,k) pairs filter 17 q=332194817 [sparse gcd] -> 1227676 surviving (A,k) pairs filter 18 q=332194931 [sparse gcd] -> 778241 surviving (A,k) pairs filter 19 q=332195047 [sparse gcd] -> 493387 surviving (A,k) pairs filter 20 q=332195159 [sparse gcd] -> 312713 surviving (A,k) pairs filter 21 q=332195293 [sparse gcd] -> 198245 surviving (A,k) pairs filter 22 q=332195393 [sparse gcd] -> 125743 surviving (A,k) pairs filter 23 q=332195503 [sparse gcd] -> 79693 surviving (A,k) pairs filter 24 q=332195641 [sparse gcd] -> 50467 surviving (A,k) pairs filter 25 q=332195761 [sparse gcd] -> 32151 surviving (A,k) pairs filter 26 q=332195863 [sparse gcd] -> 20381 surviving (A,k) pairs filter 27 q=332195987 [sparse gcd] -> 13073 surviving (A,k) pairs filter 28 q=332196127 [sparse gcd] -> 8202 surviving (A,k) pairs filter 29 q=332196229 [sparse gcd] -> 5246 surviving (A,k) pairs filter 30 q=332196349 [sparse gcd] -> 3334 surviving (A,k) pairs filter 31 q=332196463 [sparse gcd] -> 2077 surviving (A,k) pairs filter 32 q=332196577 [sparse gcd] -> 1301 surviving (A,k) pairs filter 33 q=332196707 [sparse gcd] -> 815 surviving (A,k) pairs filter 34 q=332196833 [sparse gcd] -> 512 surviving (A,k) pairs filter 35 q=332196937 [sparse gcd] -> 328 surviving (A,k) pairs filter 36 q=332197043 [sparse gcd] -> 192 surviving (A,k) pairs filter 37 q=332197169 [sparse gcd] -> 122 surviving (A,k) pairs filter 38 q=332197301 [sparse gcd] -> 81 surviving (A,k) pairs filter 39 q=332197451 [sparse gcd] -> 51 surviving (A,k) pairs filter 40 q=332197597 [sparse gcd] -> 35 surviving (A,k) pairs filter 41 q=332197699 [sparse gcd] -> 25 surviving (A,k) pairs filter 42 q=332197819 [sparse gcd] -> 19 surviving (A,k) pairs filter 43 q=332197933 [sparse gcd] -> 13 surviving (A,k) pairs filter 44 q=332198051 [sparse gcd] -> 11 surviving (A,k) pairs filter 45 q=332198159 [sparse gcd] -> 7 surviving (A,k) pairs filter 46 q=332198267 [sparse gcd] -> 4 surviving (A,k) pairs filter 47 q=332198423 [sparse gcd] -> 3 surviving (A,k) pairs filter 48 q=332198533 [sparse gcd] -> 2 surviving (A,k) pairs filter 49 q=332198639 [sparse gcd] -> 1 surviving (A,k) pairs filter 50 q=332198743 [sparse gcd] -> 1 surviving (A,k) pairs filter 51 q=332198849 [sparse gcd] -> 1 surviving (A,k) pairs filter 52 q=332198957 [sparse gcd] -> 1 surviving (A,k) pairs filter 53 q=332199067 [sparse gcd] -> 1 surviving (A,k) pairs filter 54 q=332199167 [sparse gcd] -> 1 surviving (A,k) pairs filter 55 q=332199277 [sparse gcd] -> 1 surviving (A,k) pairs filter 56 q=332199377 [sparse gcd] -> 1 surviving (A,k) pairs filter 57 q=332199509 [sparse gcd] -> 0 surviving (A,k) pairs size-bound candidates : 5685998379 pairs filters actually used : 57 filter primes : [332192873 332192977 332193089 332193203 332193383 332193529 332193629 332193751] ... [332198743 332198849 332198957 332199067 332199167 332199277 332199377 332199509] filter build : 16m3.389337584s modular survivors : 0 pairs inside B-range : 0 pairs known nontrivial solution: 6! * 7! = 10! new solutions found : 0 (A,k) pairs examined : 0 reduced kth roots : 0 full-root fallbacks : 0 exact product compares : 0 elapsed : 16m3.389441209s ====================================================================== 6. Hybrid revision 2 (recorded source body above), D=10^9 - the record run ====================================================================== searching hypothetical solutions other than (6,7,10) B range : 10^3000 .. 10^1000000000 bounds : A <= 3321928159, 2 <= k=C-B <= 33 workers : 10 filters : up to 100 exact prime-field filters hybrid : sparse polynomial-GCD mode at <= 30000000 survivors memory : dense image bitsets grouped within 16384 MiB filter 1 q=3321928171 [dense image x10 g1] -> 33379653237 surviving (A,k) pairs filter 2 q=3321928307 [dense image x10 g1] -> 18153742484 surviving (A,k) pairs filter 3 q=3321928417 [dense image x10 g1] -> 10317621414 surviving (A,k) pairs filter 4 q=3321928531 [dense image x10 g1] -> 6067538199 surviving (A,k) pairs filter 5 q=3321928661 [dense image x10 g1] -> 3657357789 surviving (A,k) pairs filter 6 q=3321928777 [dense image x10 g1] -> 2242421959 surviving (A,k) pairs filter 7 q=3321928919 [dense image x10 g1] -> 1390578257 surviving (A,k) pairs filter 8 q=3321929029 [dense image x10 g1] -> 868710336 surviving (A,k) pairs filter 9 q=3321929129 [dense image x10 g1] -> 545278518 surviving (A,k) pairs filter 10 q=3321929257 [dense image x10 g1] -> 343293928 surviving (A,k) pairs filter 11 q=3321929357 [dense image x10 g1] -> 216534691 surviving (A,k) pairs filter 12 q=3321929461 [dense image x10 g1] -> 136766212 surviving (A,k) pairs filter 13 q=3321929563 [dense image x10 g1] -> 86450089 surviving (A,k) pairs filter 14 q=3321929683 [dense image x10 g1] -> 54671311 surviving (A,k) pairs filter 15 q=3321929789 [dense image x10 g1] -> 34592570 surviving (A,k) pairs filter 16 q=3321929909 [dense image x10 g1] -> 21885141 surviving (A,k) pairs filter 17 q=3321930011 [sparse gcd] -> 13849339 surviving (A,k) pairs filter 18 q=3321930173 [sparse gcd] -> 8764451 surviving (A,k) pairs filter 19 q=3321930289 [sparse gcd] -> 5548791 surviving (A,k) pairs filter 20 q=3321930397 [sparse gcd] -> 3513991 surviving (A,k) pairs filter 21 q=3321930517 [sparse gcd] -> 2224428 surviving (A,k) pairs filter 22 q=3321930671 [sparse gcd] -> 1407795 surviving (A,k) pairs filter 23 q=3321930793 [sparse gcd] -> 890832 surviving (A,k) pairs filter 24 q=3321930893 [sparse gcd] -> 564284 surviving (A,k) pairs filter 25 q=3321931007 [sparse gcd] -> 357126 surviving (A,k) pairs filter 26 q=3321931111 [sparse gcd] -> 225918 surviving (A,k) pairs filter 27 q=3321931213 [sparse gcd] -> 142858 surviving (A,k) pairs filter 28 q=3321931313 [sparse gcd] -> 90404 surviving (A,k) pairs filter 29 q=3321931429 [sparse gcd] -> 57311 surviving (A,k) pairs filter 30 q=3321931531 [sparse gcd] -> 36289 surviving (A,k) pairs filter 31 q=3321931637 [sparse gcd] -> 23126 surviving (A,k) pairs filter 32 q=3321931763 [sparse gcd] -> 14595 surviving (A,k) pairs filter 33 q=3321931897 [sparse gcd] -> 9264 surviving (A,k) pairs filter 34 q=3321932063 [sparse gcd] -> 5928 surviving (A,k) pairs filter 35 q=3321932179 [sparse gcd] -> 3758 surviving (A,k) pairs filter 36 q=3321932353 [sparse gcd] -> 2385 surviving (A,k) pairs filter 37 q=3321932473 [sparse gcd] -> 1499 surviving (A,k) pairs filter 38 q=3321932591 [sparse gcd] -> 951 surviving (A,k) pairs filter 39 q=3321932701 [sparse gcd] -> 629 surviving (A,k) pairs filter 40 q=3321932819 [sparse gcd] -> 392 surviving (A,k) pairs filter 41 q=3321932947 [sparse gcd] -> 250 surviving (A,k) pairs filter 42 q=3321933047 [sparse gcd] -> 154 surviving (A,k) pairs filter 43 q=3321933169 [sparse gcd] -> 103 surviving (A,k) pairs filter 44 q=3321933271 [sparse gcd] -> 67 surviving (A,k) pairs filter 45 q=3321933379 [sparse gcd] -> 38 surviving (A,k) pairs filter 46 q=3321933541 [sparse gcd] -> 23 surviving (A,k) pairs filter 47 q=3321933661 [sparse gcd] -> 13 surviving (A,k) pairs filter 48 q=3321933781 [sparse gcd] -> 5 surviving (A,k) pairs filter 49 q=3321933893 [sparse gcd] -> 3 surviving (A,k) pairs filter 50 q=3321934003 [sparse gcd] -> 0 surviving (A,k) pairs size-bound candidates : 64660169462 pairs filters actually used : 50 filter primes : [3321928171 3321928307 3321928417 3321928531 3321928661 3321928777 3321928919 3321929029] ... [3321933169 3321933271 3321933379 3321933541 3321933661 3321933781 3321933893 3321934003] filter build : 3h38m8.345710959s modular survivors : 0 pairs inside B-range : 0 pairs known nontrivial solution: 6! * 7! = 10! new solutions found : 0 (A,k) pairs examined : 0 reduced kth roots : 0 full-root fallbacks : 0 exact product compares : 0 elapsed : 3h38m8.345874s