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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 3digit 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 odddigit "extra brilliant number." [Loungrides] A MATHEMATICA search confirmed the three hundred nineteen digit almostrepdigit 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]
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