# 821

This number is a prime.

The smallest prime of the first prime quadruple for which the sums of the cubes of the digits of the four primes (821, 823, 827, 829) are primes themselves (521, 547, 863, 1249). [Trotter]

The smallest prime whose reversal is a seventh power (128 = 2^{7}). [Gupta]

6! + 5! - 4! + 3! - 2! + 1!. [Lownsdale]

The smallest of the prime quadruplet which is the largest of the three 3-digit prime quadruplets {101, 103, 107, 109}, {191, 193, 197, 199} and {821, 823, 827, 829} has, as digital reversal, the number of 6-digit prime quadruplets (128). [Post]

A prime formed from the first two composite Fibonacci numbers (8,21). [Silva]

Smallest multidigit prime partial sum of number of planar graphs with minimum degree at least 1 and n nodes. Also largest known prime of its form: 0 + 1 + 2 + 7 + 22 + 109 + 680 = 821 is prime. [Post]

2^821+821^3 is the 2nd prime and the largest non-titanic prime of form 2^p+p^3, where p is a prime. The previous such prime is 157. [Loungrides]

The smallest prime in the largest 3-digit prime quadruplet, {821, 823, 827, 829}, whose sums of digits are the terms of the only double-digit quadruplet, {11, 13, 17, 19}. [Loungrides]