# 751

This number is a prime.

The largest prime that cannot be expressed as the sum of five or fewer squared composite numbers.

Chicago psychologist Doctor Robert Hartley's suite number on the TV series *The Bob Newhart Show* is 715, but has appeared as 751 due to the rearrangement of digits by set designers.

7! - 5! - 1! is also prime! [Gevisier]

The smallest multidigit prime p such that p*2^p-1 is a Woodall prime. [Gupta]

751 is not a twin prime but 7#+5#± 1, 7#-5#± 1, and 7#*5#± 1, all are twin primes. [Vrba]

The number built with "expanded notation" in the classic
book *MATHEMATICS* by David Bergamini and the Editors
of LIFE (1963, p. 194), revealing to primary-graders how
large numbers are constructed of hundreds, tens, and units.

The smallest integer with the following property: the sum of digits of 751 = the sum of digits of the 751st prime = the sum of digits of the 751st semiprime. [Sedov and Post]

The only known emirp n such that p = n*2^n-1 is a Woodall prime. [Loungrides]

751 is the smallest prime p such p and prime(p) have same set of distinct digits. [Kumar]

Both numbers 751^(7+5+1) and 751^(7*5*1) end with 751. There exists only one other known prime with this property. [Firoozbakht]

751^751 ends with 751. [Bopardikar]

The smallest emirp Honaker number corresponding to a Honaker prime, i.e., 5701. [Loungrides]

New Horizons observations of Charon (largest moon of dwarf planet Pluto) confirm previous estimates of 751 miles across. [NASA]

The smallest prime (emirp) that can be represented as the product of first n positive multiples of 5 plus 1, i.e., 5*10*15+1. [Loungrides]