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.

The sum of prime digits and composite digits of primes up to 829 are equal. Is there another prime with this property? [Sariyar]

A 829-bit integer was factored in February 2020 by Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé, and Paul Zimmermann.

1234567891*10^(k+10)+1987654321 is a palindromic prime, where k = 829. Found by Mikk Heidemaa at the University of Tartu, Estonia.