Prime Curios!: 341

341
(another Prime Pages' Curiosity)

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Chinese mathematicians (circa 500 B.C.) erroneously believed that 2(2^(n-1)-1) is not divisible by n if n is not prime. This was disproved by Sarrus in 1819 with n = 341, i.e., the smallest pseudoprime to base two.

The smallest member of the series n(n + 1 ) - 1 which, if composite, is not the product of two smaller primes in the series of the form 10k - 1 or 10k + 1. [McNamara]

341!₂ - (3+4+1) and 341!₂ + (3+4+1) are two consecutive primes with length 341 + prime(3+4+1). [Firoozbakht]

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