20150208, 13:47  #12  
"Mark"
Apr 2003
Between here and the
2·7·11·41 Posts 
Quote:


20150208, 22:32  #13 
"Antonio Key"
Sep 2011
UK
3^{2}·59 Posts 
If you reread my question you will see that I was not asking about the checkpoint file, I was referring to the file listing the eliminated candidates and their factors.

20150209, 11:02  #14 
Sep 2013
Perth, Au.
2×7^{2} Posts 
Currently when the program finds a factor it prints it on the console window and appends it to the factors file on disk. This will slow the program early in the sieve when lots of factors are found, but its not like it rewrites the whole file each time. It would be faster early in the sieve not to report factors, but if you don't write to disk you'll lose the factor information. I suppose if your only interested in the sieve file then suppressing this output would be useful. From an admin point of view you'd want to still verify the factors found. Later on in the sieve writing to the factor file will make no real difference. Let me know if you still think an option to suppress factor reporting would be worthwhile. Would be easy to implement.

20150210, 04:34  #15  
Apr 2014
7×17 Posts 
Quote:
http://factordb.com/index.php?id=100...sign+to+worker 

20150210, 19:59  #16 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·7·337 Posts 
This did not imply that C(20493)1 needs a doublecheck of primality. It was known that it is prime since 2000.
This meant "you will soon doublecheck its position in sequence OEIS sequence A140293". Additionally, if you meant the "Create time : Before March 17, 2011, 12:27 am" in "More information" section, note that all of them have been apparently entered into the factorDB up to 99,999 very long ago, before Syd started recording insertion dates. 
20150222, 02:22  #17 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·7·337 Posts 
Not quite compositorial, but "nearfactorial" primes...
All in one place for convenience: Code:
Numbers k such that k!/m1 is prime: /1 see A002982 3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, 34790, 94550, 103040, 147855 * /2 see A082671 3, 4, 5, 6, 9, 31, 41, 373, 589, 812, 989, 1115, 1488, 1864, 1918, 4412, 4686, 5821, 13830 * [20000] /3 see A139056 4, 6, 12, 16, 29, 34, 43, 111, 137, 181, 528, 2685 * [30000] ...and 98166 /4 see A139199 4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908 * 2940 /5 see A139200 5, 11, 12, 16, 36, 41, 42, 47, 127, 136, 356, 829, 1863, 2065, 2702 * 4509 /6 see A139201 4, 5, 7, 8, 11, 14, 16, 17, 18, 20, 43, 50, 55, 59, 171, 461, 859 * 2830, 3818, 5421, 5593 /7 see A139202 7, 9, 20, 23, 46, 54, 57, 71, 85, 387, 396, 606, 1121, 2484 * /8 see A139203 4, 6, 8, 10, 11, 16, 19, 47, 66, 183, 376, 507 * 1081, 1204 /9 see A139204 6, 15, 17, 18, 21, 27, 29, 30, 37, 47, 50, 64, 125, 251, 602, 611, 1184, 1468, 5570 * /10 see A139205 5, 6, 7, 11, 13, 17, 28, 81, 87, 433, 640, 647 * 798, 1026, 1216, 1277, 3825 Numbers k such that k!/m+1 is prime: /1 see A002981 0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, 110059, 150209 * /2 see A082672 2, 4, 5, 7, 8, 13, 16, 30, 43, 49, 91, 119, 213, 1380, 1637, 2258, 4647, 9701, 12258 * [20000] /3 see A089085 3, 5, 6, 8, 11, 17, 23, 36, 77, 93, 94, 109, 304, 497, 1330, 1996, 3027, 3053, 4529, 5841 * 20556, 26558, 28167 [30000] /4 see A139061 4, 5, 6, 13, 21, 25, 32, 40, 61, 97, 147, 324, 325, 348, 369 * 1290, 1342, 3167 /5 see A139058 7, 9, 11, 14, 19, 23, 45, 121, 131, 194, 735, 751 * 1316, 1372, 2084, 2562, 5678, 5758 /6 see A139063 3, 4, 10, 11, 13, 14, 17, 21, 82, 115, 165, 167, 173, 174, 208, 225, 380, 655, 1187 * 2000, 2568, 3010, 4542 /7 see A139065 11, 15, 16, 25, 35, 59, 64, 68, 82, 121, 149, 238 * 584, 912, 3349, 4111, 4324 /8 see A151913 7, 9, 10, 12, 14, 20, 23, 24, 29, 44, 108 * 2049, 3072, 4862 /9 see A137390 8, 46, 87, 168, 259, 262, 292, 329, 446, 1056, 3562, 11819, 26737 * /10 see A139071 5, 6, 11, 12, 15, 23, 26, 37, 45, 108, 112, 129, 137, 148, 172, 248 * 760, 807, 975, 1398, 5231 Numbers k such that m*k!1 is prime: 2* A076133 2, 3, 4, 5, 6, 7, 14, 15, 17, 22, 28, 91, 253, 257, 298, 659, 832, 866, 1849, 2495, 2716, 2773, 2831, 3364, 5264, 7429, 28539, 32123, 37868 * 3* A076134 0, 1, 2, 3, 4, 5, 9, 12, 17, 26, 76, 379, 438, 1695 * [6000] 4* A099350 0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579 * 1264, 2276, 2669, 4316, 4382, 4678 5* A099351 3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521 * 1279, 1750, 2204, 2473, 4193 6* A180627 0, 1, 2, 5, 8, 42, 318, 326, 1054, 2987 * 7* A180628 2, 3, 4, 5, 6, 7, 8, 12, 23, 25, 31, 57, 74, 86, 140, 240, 310, 703, 713, 796, 1028, 1102 * 1924 8* A180629 0, 1, 3, 4, 8, 33, 121, 177, 190, 276, 473, 484, 924, 937, 1722, 2626, 4077, 4464 * 9* A180630 2, 3, 12, 15, 16, 25, 30, 38, 59, 82, 114, 168, 172, 175, 213, 229, 251, 302, 311, 554 * 10*A180631 2, 3, 4, 33, 55, 95, 110, 148, 170, 612, 1155 * 2295 Numbers k such that m*k!+1 is prime: 2* A051915 0, 1, 2, 3, 5, 12, 18, 35, 51, 53, 78, 209, 396, 4166, 9091, 9587, 13357, 15917, 17652, 46127 * 3* A076679 2, 3, 4, 6, 7, 9, 10, 13, 23, 25, 32, 38, 40, 47, 96, 3442, 4048 * 4522, 4887 [6000] 4* A076680 0, 1, 4, 7, 8, 9, 13, 16, 28, 54, 86, 129, 190, 351, 466, 697, 938, 1510, *2748, 2878*, 3396, 4057, 4384 * 5* A076681 2, 3, 5, 10, 11, 12, 17, 34, 74, 136, 155, 259, 271, 290, 352, 479, 494, 677, 776, 862, 921, 932, 2211, 3927 * 4688 6* A076682 0, 1, 2, 3, 7, 8, 9, 12, 13, 18, 24, 38, 48, 60, 113, 196, 210, 391, 681, 739, 778, 1653, 1778, 1796, 1820, *2391*, 2505, 4595 * 7* A076683 3, 7, 8, 15, 19, 29, 36, 43, 51, 158, 160, 203, 432, 909, 1235, 3209 * 8* A178488 2, 4, 9, 10, 11, 12, 15, 25, 31, 46, 53, 78, 318, 615, 955 * 1646 9* A180626 2, 6, 7, 10, 13, 15, 24, 29, 33, 44, 98, 300, 548, 942, 1099, 1176, 1632, 1794, 3676, 3768 * 10*A126896 0, 1, 3, 4, 5, 23, 32, 39, 61, 349, 718, 805, 1025, 1194 * 1550, 1774 
20150224, 12:28  #18 
Sep 2013
Perth, Au.
2·7^{2} Posts 
Golden Prime Search
OEIS seems to classify:
"1" forms as "Almost* primes" and; "+1" forms as "Quasi* primes" https://oeis.org/wiki/Baseindepende..._prime_numbers I can suggest the following names: Code:
Form Description n!/k1 Almostk divisorFactorial prime n!/k+1 Quasik divisorFactorial prime k*n!1 Almostk multiplierFactorial prime k*n!+1 Quasik multiplierFactorial prime n#/k1 Almostk divisorPrimorial prime n#/k+1 Quasik divisorPrimorial prime k*n#1 Almostk multiplierPrimorial prime k*n#+1 Quasik multiplierPrimorial prime n!/(k*n#)1 Almostk divisorCompositorial prime n!/(k*n#)+1 Quasik divisorCompositorial prime k*n!/n#1 Almostk multiplierCompositorial prime k*n!/n#+1 Quasik multiplierCompositorial prime 98166!/3  1 Orial means Golden in Latin. 
20150224, 20:30  #19 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·7·337 Posts 
Well, in OEIS, "Almost" and "Quasi" prefixes sound rather arbitrary, and your fulllength names are truly cumbersome to pronounce ;).
I am not sure about "k divisorFactorial" nomenclature: they are instead factorials with some terms skipped (the shorthand form shouldn't fool, just like with compositorials: yes, n!/n# is easy to write and will be understood by humans and parsed by most programs, but what it conceptually is a product of "not all sequential" numbers, in this case, all composite numbers). Some of them are permutation numbers P_{n,k} (e.g. n!/2 or n!/6). P.S. It goes without saying (but I didn't mention it before) that fpsieve is easily modified for these forms and that's what I indeed used before primality tests. 
20150224, 23:22  #20 
Sep 2013
Perth, Au.
2·7^{2} Posts 
Maybe these terms better suit:
skipped kFactorial kFactorial skipped kPrimorial kPrimorial skipped kCombinatorial kCombinatorial This nomenclature works except when the k your dividing isn't a Prime/Composite respectively, so isn't skipped as such. Last fiddled with by TheCount on 20150224 at 23:29 Reason: Not always a skipping 
20150225, 00:24  #21 
Sep 2013
Perth, Au.
2·7^{2} Posts 
Indeed if k has prime factors with multiplicities then n#/k will be a fraction and so n#/k+/1 can't be a prime.

20150608, 12:15  #22 
Sep 2013
Perth, Au.
2×7^{2} Posts 
48934!/48934# + 1 is prime
Submitted edit to OEIS A140294. Proposed to give Daniel Heuer credit for 17258!/17257# + 1 Fully searched Compositorial up to n=45,000. Continuing to 50k. I am going to extend the "nearfactorial" sequences 3*k!+/1 [A076679, A076134] next by adding multiplier support to fpcsieve. 
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