15696RE: [PrimeNumbers] another way to calculate primes

Expand Messages
• Dec 6, 2004
It seems correct, but we can say it in an equivalent way:

the set of prime numbers = 2, 5 PLUS all odd numbers > 5, not ending by
5 and not composite.

Following your way we could perform primality test on a number N
searching odd numbers ending by 1, 3, 7, 9 and less than sqrt(N).

Moreover, considering the least significant digit:

...1 => 1 x 1 or 3 x 7 or 9 x 9
...3 => 1 x 3 or 7 x 9
...7 => 1 x 7 or 3 x 9
...9 => 1 x 9 or 7 x 7 or 3 x 3

we can limit our search to a set of the order of sqrt(N) x 2/10 or
sqrt(N) x 3/10 elements.
That is: numbers ending by 1, 3, 9 (or 1, 7, 9) if N ends by 1 and so
on.

I was wondering this: for a fixed M, are there more primes < M ending
with 3 and 7 than primes < M ending with 1 and 9?

Gianni

>-----Original Message-----
>From: Jim Doyle [mailto:ozyjim2004@...]
>Sent: Friday, December 03, 2004 1:53 AM
>Subject: [PrimeNumbers] another way to calculate primes
>
>
>Hi
>
>I'm not sure if this is a new idea but I have not come across
>it . Its based on the fact that apart from 2 and 5 all primes
>have a last digit of 1,3,7 or 9.
>
>...
>...
>
>Jim
• Show all 15 messages in this topic