[math-fun] Re: Product of three consecutive primes question

Let p < q < r denote any 3 consecutive primes. How many such p,q,r satisfy p*q*r = N^3 + 1 for some integer N ? (Above all, is it finite or infinite?)

N^3+1 = (N+1)(N^2-N+1). If that's a product of three consective primes, I bet N+1 is the middle prime. The other two would be N+a and N-b for some odd a and b; so N = (1+ab)/(1+a-b). a and b must be pretty small (to make the primes consecutive), and must be pretty big (around sqrt N), so this can't work very often. I guess that N=10 is the only instance. -- Don Reble djr@nk.ca -- This message has been scanned for viruses and dangerous content by MailScanner, and is believed to be clean.