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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