859

This number is a prime.

The largest prime that cannot be the central number in a 3-by-3 prime magic square. [Rivera]

Théorie des Nombres by Adrien-Marie Legendre contained 859 large quarto pages and was the first text to record the observation that there seemed to be a curious connection between the prime counting function and the logarithm function.

The largest 3-digit distinct-digit prime p such that replacing any of its digits with the digit 3, the result is always a prime, i.e., 359, 839, 853. Note that a concatenation of these three primes, i.e., 359853839 is also prime. [Loungrides]

The prime number 859 is the prime index of the first beastly prime (6661). [Gaydos]

There are 859 distinct-digit Honaker numbers with corresponding distinct-digit Honaker primes. [Gaydos]

The sum of the first 859 beast numbers is divisible by the beast. [Gaydos]