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Math Help - Smallest primes

  1. #1
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    Smallest primes

    Find the smallest prime greater than 10,000 and prove that it is prime.
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  2. #2
    Senior Member Tinyboss's Avatar
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    You could just do the sieve starting at 10,000. Since 10,000=100*100, it's not too hard to figure out where to begin for each prime: for instance if you want to know where to start with the prime 23, just notice that 100 = 8 (mod 23), so that 10,000 = 8*8 = 64 = 18 (mod 23). So 10,000-18=9,982 is a multiple of 23, and you can tick off 10005, 10051, 10097, and so on (though I wouldn't bother carrying it out any farther than that).

    You'd have to do this for all the primes up to 97 or so...that's 22 of them not counting 2, 3, 5 which are trivial to check. Sounds like a lot of work...there's probably a better way, but that's all I can think of right now.
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