# 319

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 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]