41

This number is a prime.

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Brittany Finch © 2004

prime(1)^π(1) + prime(2)^π(2) + ... + prime(41)^π(41) is an emirp and 41 is the only multidigit number with this property. [Firoozbakht]

2 + 3 + 5 + ... + 31 = 37 (mod 41). Note that 31, 37, and 41 are consecutive primes and 41 is the smallest nontrivial prime with this property (2 + 3 = 5 (mod 7)). [Firoozbakht]