Josh writes: << In addition to the two examples from previous messages (7 * 11 * 13 = 10^3 + 1 and 211 * 227 * 241 = 226^3 + 1), there are lots more products of three (not necessarily consecutive) primes that make one more than a cube. See http://www.research.att.com/~njas/sequences/A115403 . . . . . . .
Wouldn't you just know it, that someone had to come along and think of almost my question, and ***exactly*** what Chris asked: << . . . [Dan] asked about consecutive primes p, q, r with p*q*r = n^3 + 1 for some integer n -- I thought i'd take a crack at it without requiring consecutive, . . . . . .
Turns out the A115403 was contributed to the OEIS only last March 8, less than 5 months ago, (by one Zak Seidov). If we want to keep up, folks, we're gonna hafta start thinking just a little bit faster! --Dan