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Re: a close prime number

by dragonchild (Archbishop)
on Feb 11, 2005 at 20:41 UTC ( #430258=note: print w/ replies, xml ) Need Help??


in reply to a close prime number

What have you tried? What directions are you thinking of?

If you don't provide those items, we quite reasonably are going to consider this an attempt to get us to do your homework for you.

Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.


Comment on Re: a close prime number
Re^2: a close prime number
by Anonymous Monk on Feb 11, 2005 at 20:46 UTC
    I am thinking of using Math::Prime::Simple. The way with that was:

    @ranges = ( [ $myNum-100, $myNum+100 ] ); $primes = prime( @ranges );

    But this gives me ranges from -100 to +100 of $myNum. And I would have to parse through and check to see the 2 primenumbers smaller and greater than $myNum. Is there any nicer way?

    Thanks

      There is no way of predicting what the next prime number is, given any other number. If there was, then current cryptography methods wouldn't work. All prime number generators are, for the most part, variations on brute force. The method you're looking at is probably as good as any.

      Being right, does not endow the right to be rude; politeness costs nothing.
      Being unknowing, is not the same as being stupid.
      Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
      Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.

        Okay thanks. BTW the quotes at the end of your posts are wise and correct in my opinion.
        This node was taken out by the NodeReaper on Thu Feb 17 17:19:12 2005 (EST)
        Reason: [Revelation]: A clone of node 430391.

        For more information on this node visit: this

        There is no way of predicting what the next prime number is, given any other number. If there was, then current cryptography methods wouldn't work. All prime number generators are, for the most part, variations on brute force. The method you're looking at is probably as good as any.

        Huh?!? You're joking, aren't you? The same fact that you say "all prime number generators are, for the most part, variations on brute force" is in contradiction with the claim that "there is no way of predicting what the next prime number is, given any other number".

        More precisely if I have any isprime() sub, e.g.

        sub isprime { my $n=shift; return undef if abs $n == 1; return isprime -$n if $n<0; return 0 if $n == 0; $n%$_ or return 0 for (2..sqrt $n); 1; }
        (I'm not posting a better one for others already have, and even better ones are available elsewhere.) or the witty
        sub isprime { (1 x shift) !~ /^1?$|^(11+?)\1+$/; }
        (this is Abigail's - who else?) then a sub like this:
        sub nearest_prime { my $n=my $m=shift; return $n if isprime $n; while (1) { return $n if isprime ++$n; return $m if isprime --$m; } }
        would answer the OP's question.

        Important: not only primality testing algorithms do exist, but fast ones exist too. What in some sense there is "no way" to do is to factorize a composite number which is a different problem. But really even for the latter problem there are perfectly deterministic algorithms. "Only" it is believed to be computationally "hard" (in a mathematically precise sense), whereas the former is not. It is on this last conjecture (not proved yet!) that many cryptography methods rely.

        Since the OP did not specify the size of a problem, but gave an example with small numbers, an effective answer in terms of some efficient sieving algorithm can be given.

      You can do better than using the arbitrary range of +100/-100, (which isn't going to be good enough when your numbers get larger). Here's a an introductory explaination of prime number distribution you might find helpful.


      -- All code is 100% tested and functional unless otherwise noted.
        You can do better than using the arbitrary range of +100/-100, (which isn't going to be good enough when your numbers get larger).
        Really? Is there a range of 200 consecutive numbers within which there are no primes? My understanding was that they appeared with regular density, no matter how high you climbed.

        Update:
        And I get to answer my own question. I Googled up this webpage. It's 210 numbers to the next prime from 20831323.


        Caution: Contents may have been coded under pressure.

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