# 773

This number is a prime.

The only three-digit iccanobiF prime.

The largest three-digit unholey prime.

Replacing each digit of prime 773 with its square respectively its cube results in two new primes 49499 and 34334327. Note that this latter number is also an emirp (72343343). [De Geest]

The largest three-digit prime-digit prime. [Fellows]

The number 3 followed by 773 7's is prime. [De Geest]

The smallest prime such that adding a preceding or trailing digit will always result in a composite if we omit the case where the leading digit is zero. [Noll]

This prime is the sum of the number of 3-dimensional faces in one each of the 6 regular 4-dimensional polytopes: 5 + 8 + 16 + 24 + 120 + 600 = 773. (Equivalently, this prime is the sum of the number of vertices, i.e., 0-dimensional faces, in one each of the 6 regular 4-dimensional polytopes.) [Post]

The smallest odd number n where n + 2^{k} is
composite for all k < n. [Gudipati]

The only 3-digit prime p such that p +/- 666 are emirps. [Loungrides]

In binary 11011 + 2, 110011 + 2, 1100011 + 2, 11000011 + 2, 110000011 + 2 and 1100000011 + 2 are all prime, this one being the largest. Note that all the primes are full reptend primes in binary. [Homewood]