# 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]