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Pillai primes: primes p such that there exists an integer m such that m! + 1 is == 0 (mod p ) and p is not != 1 (mod m).
T. D. Noe and Charles R Greathouse IV, <a href="/A063980/b063980.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
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Wikipedia, <a href="https://en.wikipedia.org/wiki/Pillai_prime">Pillai prime</a>.
Named after the Indian mathematician Subbayya Sivasankaranarayana Pillai (1901-1950). - Amiram Eldar, Jun 16 2021
G. E. Hardy and M. V. Subbarao, <a href="https://www.jstor.org/stable/2695445">A modified problem of Pillai and some related questions</a>, Amer. Math. Monthly, Vol. 109, No. 6 (2002), pp. 554-559; <a href="https://web.archive.org/web/20191210172226/http://www.mathA modified problem of Pillai and some related questionsalternative link</a>, Amer. Math. Monthly 109:6 (2002), pp. 554-559.
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