For information about multifactorial primes please see Chris Caldwell's glossary page on Multifactorial Primes and his list of the top 20 Primorial and Factorial Primes.
Ken Davis has kindly agreed to keep up this page at his Multifactorial Prime Page. New data will be updated only on his site.
Multifactorials are of the form forms n!!+/-1, n!!!+/-1, n!!!!+/-1 ...
We shall call these 2-factorial plus or minus one,
3-factorial plus or minus one and so on.
| nmax tested | Current searcher | n is prime for: | |
| n!+1 | 10000+ | Caldwell | |
| n!-1 | (10000) 10900 | Bouk de Water | |
| n!!+1 | 16000 | 1,2,518 | |
| n!!-1 | 12500 | Bouk de Water | 2, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, 728,842, 888, 2328, 3326, 6404, 8670 and 9682 |
| n!!!+1 | 32600 | Steven Harvey/Dan Routman | primes |
| n!!!-1 | 34400 | Steven Harvey | primes |
| n!!!!+1 | 25,000 | Bruce Ziemienski | primes |
| n!!!!-1 | 30300 | Free | primes |
| n!5+1 | 7000 | Bouk de Water | primes |
| n!5-1 | 13300 | Bouk de Water | 3, 4, 6, 7, 8, 12, 13, 14, 27, 28, 33, 35, 44, 50,62, 64, 74, 88, 114, 140, 142, 242, 248, 262, 270, 284, 395, 473, 582, 600,634, 707, 805, 882, 907, 1008, 1152, 1243, 1853, 2340, 2410, 2703, 2793,3033, 3600, 3925, 4124, 4154, 6185, 6367, 7130, 9104, 9992, 10448, 12144 and12415. |
| n!6+1 | 33000 | Ray Ballinger | primes |
| n!6-1 | 55500 | Ray Ballinger | 12,14,54,74,102,114,302,318,366,614,1178,1188, 3110,7284,21432,21906,25848,29882,41990 |
| n!7+1 | Iago L Camboa | primes | |
| n!7-1 | 39500 | Rene Dohmen | primes |
| n!8+1 | 12700 | Marc Thibeault | primes |
| n!8-1 | 7000 | Marc Thibeault | primes |
| n!9+1 | 11000 | Bouk de Water | primes |
| n!9-1 | 11000 | Bouk de Water | primes |
| n!10+1 | 48700 | Steve Harvey | primes |
| n!10-1 | 13000 | Michael | primes |
| n!11+1 | 31000 | Michael Bell Ray Ballinger |
primes |
| n!11-1 | 29500 | Free | primes |
| n!12+1 | 17200 | Dirk Augustin | primes |
| n!12-1 | 14000 | Dirk Augustin | primes |
| n!13+1 | 17000 | Dirk Augustin | primes |
| n!13-1 | 12500 | Dirk Augustin | primes |
| n!14+1 | 6000 | Free | primes |
| n!14-1 | 6000 | Free | primes |
| n!17+1 | 40000 | Michael Bell | primes |
| n!17-1 | 25000 | Michael Bell | primes |
| n!20+1 | 20000 | Micha Fleuren | primes |
| n!20-1 | 15400 | Micha Fleuren | primes |
| n!21+1 | 8500 | Micha Fleuren | primes |
| n!21-1 | 8500 | Micha Fleuren | primes |
| n!22+1 | 17300 | Micha Fleuren | primes |
| n!22-1 | 17300 | Micha Fleuren | primes |
| n!23+1 | 20000 | Michael Lau | primes |
| n!24+1 | 20000 | Didier BOIVIN | primes |
| n!100+-1 | Hans Rosenthal | ||
| n!101+-1 | Hans Rosenthal |
To test for multifactorial primes, you may use primeform