Prime numbers

1. Jul 22, 2014

wellorderingp

So it was my observation that all the prime numbers I saw ended with digits 1,3,7,9.Is this true for all primes? Is it proved?

2. Jul 22, 2014

wellorderingp

With an exception to 5

3. Jul 22, 2014

Char. Limit

Consider: With the exception of 2, no primes can be even, as if they are even, then they are divisible by 2.

Therefore, all primes must end in 1, 3, 5, 7, or 9.

Consider: With the exception of 5, no primes can end in 5, as if they do so, then they are a multiple of 5.

Therefore, all primes must end in 1, 3, 7, or 9.

So... yes.

If you need a proof of either of the considered statements, I'm sure it wouldn't be too difficult.

4. Jul 22, 2014

dkotschessaa

bah, beat me to it. :)

5. Jul 22, 2014

wellorderingp

Yeah that was pretty simple :) thanks anyways

6. Jul 22, 2014

Char. Limit

Simple, maybe, but it's still helpful for prime identification. Considering that just those two little rules invalidate over 60% of all natural numbers from being prime, it allows you (or a computer) to focus more easily upon the other 40%.

7. Jul 22, 2014

dkotschessaa

8. Jul 22, 2014

micromass

Staff Emeritus
Interesting. This means to me that there are about as many primes that end in 3, as there are primes that end in 1 (or 7 or 9). I wonder if this has been proven.

9. Jul 22, 2014

micromass

Staff Emeritus