Prime numbers and primality testing Yahoo Group primo-factorials =============================================== mikeoakes2@aol.com Message 1 of 2 Apr 3, 2003 ----------------------------------------------- A neologism, but I don't know what better to call them:- n! + n# + 1 is prime for n=1,2,3,4,5,6,8,17,18,24,95,96,142,1022,1120*,1580*,6942* n! + n# - 1 is prime for n=2,3,4,5,8,17,23,26,35,82,47,100,147,183,271,492,708,1116*,1538*,2491*,4207*, 4468* n! - n# + 1 is prime for n=4,6,7,8,10,20,21,26,101,119,172,409,621,1043,1204*,1283*,1673*,2003*,4336*,5 773* n! - n# - 1 is prime for n=4,5,20,92,106,266,308,343,583,597,903,1021,1239*,1314*,2458*,6160* These forms have the same property as the factorials and primorials in that they are guaranteed to have no prime factors <= n, and so generate more primes than similar numbers of their size; they have nothing much else to commend them, other than their simple formulae. All numbers with less than 2900 digits have been proved prime with Marcel Martin's Primo 2.0.0. The ones marked with * are only Lucas and Fermat pseudoprime according to PFGW; the smallest is 1116!+1116#-1, with 2919 digits; this and several others are good Primo candidates (anyone?). The largest is 6942!+6942#+1 with 23656 digits; this and the 5 others with 10000+ digits are being submitted to Henri Lifchitz's PRP Top 5000. The search was stopped after n=7039 and I have no plans to continue. Anyone? Mike Oakes =============================================== Barbara and Joe Message 2 of 2 Apr 7, 2003 ----------------------------------------------- I cannot believe it. I've been silently investigating these numbers for only a couple of weeks and up pops this! harrumph! You won't stop me you know! Joe. :-) -----Original Message----- From: mikeoakes2@... To: primenumbers@yahoogroups.com Date: 04 April 2003 08:35 Subject: [PrimeNumbers] primo-factorials A neologism, but I don't know what better to call them:- n! + n# + 1 is prime for n=1,2,3,4,5,6,8,17,18,24,95,96,142,1022,1120*,1580*,6942* n! + n# - 1 is prime for n=2,3,4,5,8,17,23,26,35,82,47,100,147,183,271,492,708,1116*,1538*,2491*,4207*, 4468* n! - n# + 1 is prime for n=4,6,7,8,10,20,21,26,101,119,172,409,621,1043,1204*,1283*,1673*,2003*,4336*,5 773* n! - n# - 1 is prime for n=4,5,20,92,106,266,308,343,583,597,903,1021,1239*,1314*,2458*,6160* These forms have the same property as the factorials and primorials in that they are guaranteed to have no prime factors <= n, and so generate more primes than similar numbers of their size; they have nothing much else to commend them, other than their simple formulae. All numbers with less than 2900 digits have been proved prime with Marcel Martin's Primo 2.0.0. The ones marked with * are only Lucas and Fermat pseudoprime according to PFGW; the smallest is 1116!+1116#-1, with 2919 digits; this and several others are good Primo candidates (anyone?). The largest is 6942!+6942#+1 with 23656 digits; this and the 5 others with 10000+ digits are being submitted to Henri Lifchitz's PRP Top 5000. The search was stopped after n=7039 and I have no plans to continue. Anyone? Mike Oakes ============================================== Cached by Georg Fischer at Nov 14 2019 12:46 with clean_yahoo.pl V1.4