Re: [math-fun] concatenated primes

David Wilson wrote:

Is there an infinite sequence of positive integers whose distinct pairwise concatenations are all primes?

begin smart-alek { Yes. Sloane's A000012. } end smart-alek But, is there an infinite _set_ of positive integers...? That one might be hard to answer, especially if there is. Suppose there were, and an oracle gave the least two elements of the set, a_1 and a_2. Then there would be an infinite set of numbers b_k, such that b_k,a_1 and b_k,a_2 are prime. Surely that's harder to prove than the twin-prime conjecture. -- Don Reble djr@nk.ca