I took a sample of the first hundred prime numbers and looked at their end digits and found this:

1 - 24

2 - 1

3 - 26

5 - 1

7 - 24

9 - 24

Of course this doesn't exclusively work, as applied to Base-10. A prime number is still prime what ever base you choose to use. In Base-2 (binary) just as in Base-10, there is no such thing as an even prime, for all even numbers are divisible by 2. The thing is though, that ALL even numbers including 2 end in 0.

Again, I took a sample of the first hundred prime numbers and looked at their end digits and found this:

0 - 1

1 - 99

Actually I didn't really need to since it was obvious, but it was still useful in testing the functionality of Excel. The eighty-first prime of 419 works out to be 110100011 for instance.

1 - 21

2 - 1

3 - 26

5 - 26

7 - 26

In Base-16, they fall into these end digits:

1 - 11

2 - 1

3 - 13

5 - 13

7 - 13

9 - 10

B - 13

D - 13

F - 13

B D F? Well in Base-16 our standard number set doesn't extend far enough. The symbols B D and F stand in place for 11, 13 and 15. 16 in Base-16 of course is one lot of sixteen and no ones and therefore is written 10. 503 which is the ninety-seventh prime comes out to be 1F7 in Base-16.

I didn't really find what I was looking for and to be honest a sample size of only 100 primes didn't really help me much but a sample size up to 1,000,000,000 yields the following results for the end digit in Base-10:

1 - 12711386 (24.999%)

2 - 1 (negligible)

3 - 12712499 (25.001%)

5 - 1 (negligible)

7 - 12712314 (25.001%)

9 - 12711333 (24.999%)

I know that this sounds dumb but I suspect that for all Bases-N, there is either no preference for the last digit towards infinity or that for all Bases-N there is an exceptionally weak tendency for the spread of the last digit to display a normal distribution across all the end digits of the base (or odd ones if it's an even base).

My problem is that I don't have the mathematical tools to be able to prove either case for all bases-n to infinity and I don't know if anyone has even written a paper on the subject. Does this have something to do with general number theory or is something else going on?

I hope that this post acts as a fly trap and people leave me some answers.

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