This problem came out of a problem being worked on by Gary Darby. Is there an infinite sequence of positive integers whose distinct pairwise concatenations are all primes? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"
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
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David Wilson -
Don Reble