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Why is it so?

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  • kadhirvel
    For prime(N)if gap == 1 && N % 10 == 1 then N % 15 = 11 always.eg.,11, 41,71..... && N % 10 == 7 then N % 15 = 2 always.eg.,17, 107,137... && N % 10 == 9
    Message 1 of 2 , Jun 2, 2006
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      For prime(N)if gap == 1 && N % 10 == 1 then N % 15 = 11 always.eg.,11, 41,71.....
      && N % 10 == 7 then N % 15 = 2 always.eg.,17, 107,137...
      && N % 10 == 9 then N % 15 = 14 always.eg.,29,59,149....

      For all prime 2 plays the same role ie.,N % 2 = 1 always.

      But 3,5 && 15 plays a different role accord with the gap.Don't mistake
      me if i asked anything silly.But u guys have to definitely answer this.

      Send instant messages to your online friends http://uk.messenger.yahoo.com

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    • Thomas Hadley
      ... mistake ... this. I assume by gap==1 you mean that N and N+2 are both primes. Let s look at your first example: N%10==1 if N%10==1 then N%15==(1,6 or 11).
      Message 2 of 2 , Jun 2, 2006
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        kadickv@... wrote on 06/02/2006 09:38:54 AM:

        > For prime(N)if gap == 1 && N % 10 == 1 then N % 15 = 11
        > always.eg.,11, 41,71.....
        > && N % 10 == 7 then N % 15 =
        > 2 always.eg.,17, 107,137...
        > && N % 10 == 9 then N % 15 = 14
        > always.eg.,29,59,149....
        >
        > For all prime 2 plays the same role ie.,N % 2 = 1 always.
        >
        > But 3,5 && 15 plays a different role accord with the gap.Don't
        mistake
        > me if i asked anything silly.But u guys have to definitely answer
        this.

        I assume by gap==1 you mean that N and N+2 are both primes. Let's look
        at your first example: N%10==1

        if N%10==1 then N%15==(1,6 or 11).
        Case 1: N%15==1, then (N+2)%15==3 and N+2 is divisible by 3
        Case 2: N%15==6, and N is divisible by 3
        Case 3: N%15==11, N+2%15==13 and neither is divisible by 3 so both could
        be primes.
        So for twin primes N and N+2, where N%10==1, N%15 must be 11.

        You can work out your other examples with similar "mod 3" tests.

        Tom

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