fpcsieve version 0.1.1 released

[rogue]

Originally Posted by TheCount

Worth a try. I'd love to get a GPU sieve for Compositorial. I could have my GPU sieving while PRP testing on my CPU.

fpsievecl? I didn't know you'd extended it to Primorial. If you hadn't yet I would extend to Primorial while adding Compositorial. We can see if it's worthwhile after its implemented.

Is v1.0.8 the latest version? If so I already have it downloaded and know how to fix a bug:
http://www.primegrid.com/forum_threa...rap=true#80600

If Compositorial implemented would the new program be called fpcsievecl? I'd add a new GitHub repo.

I tried an OpenCL primorial sieve, but the problem with was extra I/O between the GPU and CPU and more global memory access. For compositorial each chunk of work in the GPU would require less I/O as fewer primes would be sent in each chunk than for primorial. As I think about it, it might not be any faster.

[Antonio]

Originally Posted by TheCount

You can use -c option to set the checkpoint period, default is every 5 minutes. Set to 0 if you don't want it to periodically checkpoint.
I wouldn't think writing a checkpoint file would affect performance much.

If you re-read 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.

[TheCount]

Originally Posted by Antonio

If you re-read 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.

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 re-writes 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.

[pdazzl]

Originally Posted by Batalov

I've briefly searched google for "Daniel Heuer compositorial" and I think some traces (and possibly DH's limits) can be found in the archives of the primeform yahoo group. E.g. this (about C(20493)-1 which you will soon double-check) ...and this appears to be all of his messages (API of yahoo groups changed so many times over years; the new API is so inconvenient).

Daniel was active in many curious projects. I stumble over his decade old contributions in many areas.

Maybe Paul has Daniel's contacts? Paul "was always there", as they say.

Yes

http://factordb.com/index.php?id=100...sign+to+worker

[Batalov]

Originally Posted by Batalov

... (about C(20493)-1 which you will soon double-check) ...

This did not imply that C(20493)-1 needs a double-check of primality. It was known that it is prime since 2000.
This meant "you will soon double-check 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.

[Batalov]

Not quite compositorial, but "near-factorial" primes...
All in one place for convenience:

Numbers k such that k!/m-1 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

[TheCount]

OEIS seems to classify:
"-1" forms as "Almost-* primes" and;
"+1" forms as "Quasi-* primes"
https://oeis.org/wiki/Base-independe..._prime_numbers

I can suggest the following names:

Form           Description
n!/k-1         Almost-k divisor-Factorial prime
n!/k+1         Quasi-k divisor-Factorial prime
k*n!-1         Almost-k multiplier-Factorial prime
k*n!+1         Quasi-k multiplier-Factorial prime
n#/k-1         Almost-k divisor-Primorial prime
n#/k+1         Quasi-k divisor-Primorial prime
k*n#-1         Almost-k multiplier-Primorial prime
k*n#+1         Quasi-k multiplier-Primorial prime
n!/(k*n#)-1    Almost-k divisor-Compositorial prime
n!/(k*n#)+1    Quasi-k divisor-Compositorial prime
k*n!/n#-1      Almost-k multiplier-Compositorial prime
k*n!/n#+1      Quasi-k multiplier-Compositorial prime

Well done Batalov on your Almost-k divisor-Factorial prime
98166!/3 - 1

Orial means Golden in Latin.

[Batalov]

Well, in OEIS, "Almost-" and "Quasi-" prefixes sound rather arbitrary, and your full-length names are truly cumbersome to pronounce ;-).

I am not sure about "k divisor-Factorial" 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.

[TheCount]

Maybe these terms better suit:
skipped k-Factorial
k-Factorial
skipped k-Primorial
k-Primorial
skipped k-Combinatorial
k-Combinatorial

This nomenclature works except when the k your dividing isn't a Prime/Composite respectively, so isn't skipped as such.

[TheCount]

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.

[TheCount]

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 "near-factorial" sequences 3*k!+/-1 [A076679, A076134] next by adding multiplier support to fpcsieve.