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Pillai prime : ウィキペディア英語版
Pillai prime
In number theory, a Pillai prime is a prime number ''p'' for which there is an integer ''n'' > 0 such that the factorial of ''n'' is one less than a multiple of the prime, but the prime is not one more than a multiple of ''n''. To put it algebraically, n! \equiv -1 \mod p but p \not\equiv 1 \mod n. The first few Pillai primes are
:23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, ...
Pillai primes are named after the mathematician Subbayya Sivasankaranarayana Pillai, who asked about these numbers. Their infinitude has been proved several times, by Subbarao, Erdős, and Hardy & Subbarao.
==References==
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