Hacker News new | past | comments | ask | show | jobs | submit login

> https://user-images.githubusercontent.com/2993947/28248599-d...

I see a pattern in this image. There are twelve columns, and most of the primes seem to occur in 4 of them.

What's the name of this?




In base 12 those are just the columns for 1, 5, 7, and 11, the only numbers between 1 and 12 that aren't divisible by any of 12s factors. If you do this for any base the prime numbers will fall in columns like those.

Note that there aren't any prime numbers ending in 2 or 5 in base 10 (except 2 and 5), in base 12 it would be the same for numbers ending in 2, 3, 4, 6, 8, 9 and 10.



The numbers in the other columns are multiples of 2 or 3, so you wouldn't expect to see any primes in those columns other than 2 and 3 themselves.


The unique prime factorisation of 12.

12 factors into 2, 2 and 3. If a column is index 2n or 3n it will never contain a prime after the first row. The columns that match that here are: 2, 3, 4, 6, 8, 10, 12. The columns that don't are 1, 5, 7, 11 - your four.


Math?

Primes will only appear in columns whose index is coprime with 12. That's because 12n+2 is divisible by 2. 12n+3 by 3, etc for 12n+4, 12n+6, 12n+8, 12n+9, 12n+10. (For n>0. that's why there are primes on the first line)


Not exactly what you are seeing but check this as well:

https://en.wikipedia.org/wiki/Ulam_spiral




Consider applying for YC's Spring batch! Applications are open till Feb 11.

Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: