# Patterns in Prime Numbers? **URL:** \ **Category:** Factual Questions\ **Created:** [April 13, 2003, 4:59pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461 "2003-04-13T16:59:19Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![I\_Brian](https://avatars.discourse-cdn.com/v4/letter/i/c89c15/32.png) [@I\_Brian](https://boards.straightdope.com/u/I_Brian)\ **Post date:** [April 13, 2003, 4:59pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/1 "2003-04-13T16:59:19Z")
I saw an article on the [nature.com](http://nature.com) stating that there is no recognised pattern for Prime Numbers - but I’ve also seen elsewhere that the are many patterns of Prime Numbers. Could someone please advise which is the proper position? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 13, 2003, 5:06pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/2 "2003-04-13T17:06:15Z")
There are many small-scale patterns inside the prime numbers, but there’s no large-scale pattern that would allow you to easily predict the (n + 1)th prime given the first n. You can read a lot more about it in [this thread](http://boards.straightdope.com/sdmb/showthread.php?s=&threadid=166276). ---
**Author:** ![I\_Brian](https://avatars.discourse-cdn.com/v4/letter/i/c89c15/32.png) [@I\_Brian](https://boards.straightdope.com/u/I_Brian)\ **Post date:** [April 13, 2003, 5:42pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/3 "2003-04-13T17:42:04Z")
Thanks for that - I now know a lot more. 🙂 The reason I asked is because a few years back I was messing about with numbers when I found a pattern to the primes - much better than Ulam’s spiral. Trouble is, I can’t represent it in precise mathematical terms. Which means that there is no way of knowing if it’s even relevant. I figure that someone _must_ have discovered this pattern - probably in the 17th or 18th century. I guess the best bet is to place it in a novel I’m hoping to put forward for publishing this year - have a scene where in a few lines I have a main character playing with numbers. I guess when I’m finally a published author I’ll know whether the pattern is relevant or not. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 13, 2003, 5:47pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/4 "2003-04-13T17:47:34Z")
Give us some description of the pattern, and we can tell you much more about it than you wanted to know. ---
**Author:** ![I\_Brian](https://avatars.discourse-cdn.com/v4/letter/i/c89c15/32.png) [@I\_Brian](https://boards.straightdope.com/u/I_Brian)\ **Post date:** [April 13, 2003, 7:47pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/5 "2003-04-13T19:47:45Z")
I was sort of preferring to find what patterns have already been discovered - but it doesn;t really matter. I doubt that I have found anything originally, but I do find the sequence interesting. Of course, I can’t predict large primes from it either. I guess that would be the only really relevant achievement. Thanks for answering anywayy. 🙂 ---
**Author:** ![The\_Man\_With\_The\_Golden\_Gun](https://avatars.discourse-cdn.com/v4/letter/t/dc4da7/32.png) [@The\_Man\_With\_The\_Golden\_Gun](https://boards.straightdope.com/u/The_Man_With_The_Golden_Gun)\ **Post date:** [April 13, 2003, 10:01pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/6 "2003-04-13T22:01:35Z")
The only thing that’s even close that I can think of is that all primes, with one exception, are odd numbers. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [April 14, 2003, 1:27am UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/7 "2003-04-14T01:27:55Z")
Many people have spent many years looking for patterns in the primes, and none have been found. It’s much more likely that you made a mistake when you thought you found a pattern than that you actually found one. It’s also possible that what you did was find some pattern that worked for a couple of dozen primes, but you didn’t check any further. That could happen, but it’s not very interesting. ---
**Author:** ![The\_Peyote\_Coyote](https://avatars.discourse-cdn.com/v4/letter/t/5f8ce5/32.png) [@The\_Peyote\_Coyote](https://boards.straightdope.com/u/The_Peyote_Coyote)\ **Post date:** [April 14, 2003, 2:01am UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/8 "2003-04-14T02:01:58Z")
To take it a little further, The Man With The Golden Gun, all primes have 1, 3, 7, or 9 as the final digit. It’s interesting this thread came up. I was bored at work on Friday and did a Sieve of Erasothenes for the first 300 numbers. There was no discernible pattern that I could detect. ---
**Author:** ![N9IWP](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/n9iwp/32/3154_2.png) [@N9IWP](https://boards.straightdope.com/u/N9IWP)\ **Post date:** [April 14, 2003, 2:06am UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/9 "2003-04-14T02:06:46Z")
slight hijack, but a recent proof about primes: [http://www.olimu.com/Notes/GoldstonYildirim.htm](http://www.olimu.com/Notes/GoldstonYildirim.htm) Brian ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [April 14, 2003, 10:04pm UTC](https://boards.straightdope.com/t/patterns-in-prime-numbers/168461/10 "2003-04-14T22:04:25Z")
If you generate the differences between adjacent primes up to some number N, and look at the number of occurrances of each difference, there are peaks at multiples of 6. For example, with N = 1,000,000 the numbers of occurances of adjacent primes separated by M are: M: number 2: 8169 4: 8143 6: 13549 8: 5569 10: 7079 12: 8005 14: 4233 16: 2881 18: 4909 20: 2401 22: 2172 24: 2682 The pattern seems to continue. This is probably just a generalization of the peaking at multiples of two.