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Another one eliminated:
[CODE]Sm(1033) = 30915171019253321813 * C3005[/CODE] |
1 Attachment(s)
I have trial factored the first 25000 Smarandache numbers to 2^32 with a C program. The factors are attached.
PrimeForm/GW has prp tested the cofactor of the first 10000, and those from 10000 to 25000 which have exactly one prime factor below 2^32. No probable semiprimes were found beyond the two earlier reported: Sm(5053) and Sm(9706). 39 complete factorizations up to Sm(200) were rediscovered. 25 complete factorizations above Sm(200) were found: [CODE]Sm(203) = 3 * 521 * p497 Sm(265) = 5 * 17 * 887 * 1787 * p678 Sm(279) = 3^2 * 458891 * p722 Sm(327) = 3 * 23 * 132861611 * p863 Sm(343) = 19 * 271 * 1601 * p914 Sm(345) = 3 * 5 * 37 * 47 * 67 * 157 * 441121 * 43455173 * 1503598049 * 2913393619 * p886 Sm(452) = 2^2 * 3 * 67 * 163 * 3023 * 83177 * p1234 Sm(461) = 3 * 23^2 * 1033 * p1268 Sm(572) = 2^2 * 3 * 2399 * p1603 Sm(601) = 2749 * 3403013 * 33226397 * 3222045163 * p1668 Sm(780) = 2^2 * 3 * 5 * 17^2 * 73 * 167 * 229 * p2221 Sm(872) = 2^6 * 3^2 * p2505 Sm(1386) = 2 * 3^2 * 19 * 269 * 12301 * prp4428 Sm(1927) = 7^2 * 13 * prp6598 Sm(3231) = 3^2 * 50411 * prp11811 Sm(3418) = 2 * 7 * 752933 * prp12558 Sm(3506) = 2 * 3 * 34693 * 186227 * 204749 * prp12901 Sm(5053) = 133283 * prp19099 Sm(5417) = 3^2 * 19 * prp20558 Sm(5677) = 17^2 * 7307 * 19507 * prp21590 Sm(6182) = 2 * 3^3 * 29 * 277 * prp23615 Sm(6419) = 3 * 61 * 6827 * 2368097 * 113970541 * prp24548 Sm(7582) = 2 * 13 * 17 * 31 * prp29216 Sm(8550) = 2 * 3^2 * 5^2 * 7 * 3499 * 307019 * 1551997 * prp33074 Sm(9706) = 2 * prp37716[/CODE] Marcel Martin's Primo proved the first 12 cofactors. I am not planning to prove or prp test more cofactors. |
Starting from Jens' list I can eliminate the following candidates:
[CODE]133 8223519074965787731 391 269534025881.1944200997131 463 95762360557419696305637209522797 631 414941628631826493984534937401473 649 877026198670416511 787 46110336443 859 77278117165680372333434870566009 1027 35488519258785497579 1033 30915171019253321813 1039 1479264257587679378617 1207 6176528903 1561 43008171535331 1609 129787493421373 1783 55786004333 1807 738921181 1861 1471795943419 1939 10981653341127770593 1951 891704872753975021087 1963 15654967526938910563 1999 11687073721669454909 2029 42457568152889999 2107 5135394736173493133 2191 434290438959877 2539 4840263101 2659 17678395741 3121 4745966107 3289 1787896747099 3547 222029309596931 3619 1685013448673 3673 465890314573 3883 47784961208459 3907 7663417791922241 4261 32322505871 4393 7446261457 4429 264146732728106877929671 4477 145122725496587 4549 9457516676479 4663 279168988896034784147 4711 3059843006852143 4717 7436263183 4897 37089928868738827 [/CODE] This leaves the following as possible semiprimes between 97 and the next confirmed member Sm(5053): [CODE]691 1051 1291 1651 1657 1831 2041 2047 2377 2383 2491 2761 3007 3163 3391 3493 3571 3937 3991 4057 4087 4141 4213 4399 4819 4831 4873 [/CODE] In each case I have run at least 100 curves with b1=10000. |
828297113610116869 | Sm(1291)
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I've eliminated 691 and 1051:
[CODE] 691 1304238680165623831238651513722972177904593843651 1051 94182284179957932178843944956212141 [/CODE] |
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