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Arbitrarily Long Progressions of Primes

  • 09-05-2004 3:34pm
    #1
    ecksor
    Moderators, Social & Fun Moderators Posts: 10,501 Mod ✭✭✭✭


    A proof that arbitrarily long lists of primes in arithmetic progression exist, link at the bottom of the post since it gives away the answer to the puzzle I'm going to post.

    I got interested in this several months back when I came across a New Scientist Enigma puzzle that went something like the following.

    "I have a list of 10 primes in arithmetic progression. The difference between each term is the smallest possible for a list of 10 primes in arithmetic progression, and the first term is smaller than the difference between each term. Find the first term and the difference between each term."

    So, if we call it a, a+r, a+2r, ..., a+9r the question is to find a and r.

    Link at http://mathworld.wolfram.com/news/2004-04-12/primeprogressions/

    (the other mathworld references on primes in arithmetic progression give away the asnwer too :dunno: )


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