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


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