

A055939


Primes p such that p  ((p1)/2)! + 1.


3



7, 11, 19, 43, 47, 67, 79, 103, 127, 131, 163, 179, 191, 199, 227, 263, 347, 367, 383, 419, 431, 443, 479, 491, 503, 523, 563, 571, 599, 607, 619, 631, 683, 691, 727, 739, 743, 787, 823, 839, 863, 887, 947, 991, 1019, 1051, 1087, 1091, 1123, 1151, 1187
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OFFSET

1,1


COMMENTS

p  (p1)! +1 iff p is a prime (Wilson's theorem). Note: all of the above primes are congruent to 3 (mod 4).


REFERENCES

J. B. Cosgrave, A MersenneWieferich Odyssey, Manuscript, May 2022. See Section 18.5.


LINKS



MATHEMATICA

Select[ Range[ 1225 ], PrimeQ[ # ] && Mod[ ((#  1)/2)! + 1, # ] == 0 & ]
Select[Prime[Range[200]], Divisible[((#1)/2)!+1, #]&] (* Harvey P. Dale, Dec 17 2014 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



