# 319

This number is a composite. Selfridge showed that among the partitions of n into distinct primes, the one having the maximum product of parts is not necessarily one of those with the maximum number of parts. The smallest case being 319 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 23 + 29 + 31 + 37 + 41 + 47 + 53 and 319 = 3 + 5 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47. The smallest of only two 3-digit “extra brilliant numbers,” i.e., 319 = 11 * 29, 2911 = 41 * 71, 4171 = 43 * 97. [Loungrides] The smallest 3-digit brilliant number, (319 = 29 * 11), whose the prime factors, (29, 11), create another brilliant number, 2911=41*71, and also the prime factors create a third brilliant number, i.e., 4171 = 43 * 97. We can say that 319 is the only odd-digit "extra brilliant number." [Loungrides] A MATHEMATICA search confirmed the three hundred nineteen digit almost-repdigit prime consisting of three hundred eighteen 3's followed by the digit 1. The closed formula for this term in the sequence is given by ((10^(319)-7)/3. [Schiffman] The smallest non-palindromic semiprime such that all permutations of concatenations with its factors are semiprimes, i.e., 319 = 11 * 29 and 1131929, 2931911, 3191129, 3192911, 1129319, 2911319 are all semiprimes. [Sariyar]

(There is one curio for this number that has not yet been approved by an editor.)