829

This number is a prime.

+ The smallest prime factor of the smallest composite 2 and 3-SPRP (strong probable prime).

+ The largest member in a set of twin primes generated by the formula (N^3 + 11N) ± 1, for N = 1 to 9. [Homewood]

+ The largest 3-digit prime abc with distinct digits such that a^a + b^b + c^c is prime. [Loungrides]

+ The summatory Liouville function reaches a maximum value of 829 in the region where the Pólya conjecture first fails.

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