# Prime numbers and "prim" numbers **URL:** \ **Category:** Factual Questions\ **Created:** [January 19, 2012, 3:30am UTC](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971 "2012-01-19T03:30:36Z")\ **Posts on this page:** 5\ **Page:** 2
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 21, 2012, 10:24pm UTC](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971/21 "2012-01-21T22:24:32Z")
If I understand your question (and I’m not sure I do), the answer is that the density of primes of the form 6n+1 and of the form 6n-1 are the same. About half the primes less than any large x are of the form 6n+1 and half of the form 6n-1. See [here](http://primes.utm.edu/notes/Dirichlet.html) or [here](http://en.wikipedia.org/wiki/Analytic_number_theory#Multiplicative_number_theory). ---
**Author:** ![The\_Second\_Stone](https://avatars.discourse-cdn.com/v4/letter/t/bbe5ce/32.png) [@The\_Second\_Stone](https://boards.straightdope.com/u/The_Second_Stone)\ **Post date:** [January 21, 2012, 11:41pm UTC](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971/22 "2012-01-21T23:41:48Z")
Only 7 is a prim number, because it’s leg is crossed. Or sitting up straight if you look from the side. All the others are obscene! ---
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [January 22, 2012, 3:29pm UTC](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971/23 "2012-01-22T15:29:50Z")
> [@Thudlow\_Boink](#): > > If I understand your question (and I’m not sure I do), the answer is that the density of primes of the form 6n+1 and of the form 6n-1 are the same. About half the primes less than any large x are of the form 6n+1 and half of the form 6n-1. See [here](http://primes.utm.edu/notes/Dirichlet.html) or [here](http://en.wikipedia.org/wiki/Analytic_number_theory#Multiplicative_number_theory). I mean, instead of counting the prime density in (1,2,3,4,5,6,7,8,9,10,11,12,…), count the density in (5,7,11,13,17,19,23,25,29,31,…) Since you’re looking at only a third of all numbers, do you modify the logarithmic interval three times as steep, or do you use some other function? ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 22, 2012, 4:43pm UTC](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971/24 "2012-01-22T16:43:27Z")
That’s easy: since the second list contains all the same primes as the first list (except for 2 and 3), but only a third as many numbers altogether (up to any particular x), the prime density of the second list is just like the prime density of the first, times three. The fact I referred to is deeper and less obvious: that the primes in your second list are, in a sense, equally distributed between {5, 11, 17, 23, 29, 35, …} and {7, 13, 19, 25, 37, …}. ---
**Author:** ![obfusciatrist](https://avatars.discourse-cdn.com/v4/letter/o/4af34b/32.png) [@obfusciatrist](https://boards.straightdope.com/u/obfusciatrist)\ **Post date:** [January 22, 2012, 5:06pm UTC](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971/25 "2012-01-22T17:06:06Z")
> [@Great\_Antibob](#): > > In these cases, it helps to know WHY things work. Just wanted to say thank for such a lucid (several in the thread but yours in particular) explanation. [Previous page](https://boards.straightdope.com/t/prime-numbers-and-prim-numbers/609971.md?page=1)