p is prime precisely when p
divides (p-1)!+1
- (2-1)!+1 = 1!+1 = 2
- (3-1)!+1 = 2!+1 = 3
- (4-1)!+1 = 3!+1 = 7
- (5-1)!+1 = 4!+1 = 25 = 5*5
- (6-1)!+1 = 5!+1 = 121 = 11*11
- (7-1)!+1 = 6!+1 = 721 = 7*103
- (8-1)!+1 = 7!+1 = 5041 = 71*71
- (9-1)!+1 = 8!+1 = 40321 = 61*661
- (10-1)!+1 = 9!+1 = 362881 = 19*71*269
- (11-1)!+1 = 10!+1 = 3628801 = 11*329891
- (12-1)!+1 = 11!+1 = 39916801
- (13-1)!+1 = 12!+1 = 479001601 = 13*13*2834329
- (14-1)!+1 = 13!+1 = 6227020801 = 83*75024347
- (15-1)!+1 = 14!+1 = 87178291201 = 23*3790360487
- (16-1)!+1 = 15!+1 = 1307674368001 = 59*479*46271341
- (17-1)!+1 = 16!+1 = 20922789888001 = 17*61*137*139*1059511
- (18-1)!+1 = 17!+1 = 355687428096001 = 661*537913*1000357
- (19-1)!+1 = 18!+1 = 6402373705728001 = 19*23*29*61*67*123610951
- (20-1)!+1 = 19!+1 = 121645100408832001 = 71*1713311273363831
- etc