## Why is it so?

Expand Messages
• 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 7:38 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.

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

[Non-text portions of this message have been removed]
• ... 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 10:57 AM
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

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

[Non-text portions of this message have been removed]
Your message has been successfully submitted and would be delivered to recipients shortly.