Talk:Successive prime differences
References
Could you please add a title to the references as well as the link. Thanks. --Paddy3118 (talk) 15:43, 28 April 2019 (UTC)
Different results for 6,4,2
I am getting slightly different results for the last group than the Python example and am finding it hard to see where I may be wrong. I am finding 337 groups. Am I just mising something? --Thundergnat (talk) 01:20, 27 April 2019 (UTC)
Doh! It's me, I glossed over the 'successive' part of the problem. Update to follow. --Thundergnat (talk) 01:25, 27 April 2019 (UTC)
Task background
It's my birthday soon so I googled my age and found:
- It's a prime.
- It's a twin prime.
I searched Rosetta Code and found that there was no twin prime task! (I had expected that someone would have already started it). I resolved to wait until closer to my birthday then put up a twin primes task and left it at that.
A few days later I started to think of what a generalisation around the idea of twin primes would be and hit on a difference; then multiple differences; then really liked how my solution to generating a sliding group of <count> items from a list actually did come from the Python fundamentals:
- <lang python>zip(*(lst[n:] for n in range(count)))</lang>
I finished the code and played with the differences then firmed up what the task details would become. I wrote the task and added extra explanations and emphasis to try and help the reader grasp the details, then went to bed.
Today I've just done a search of the primes generated from differences of 2, 4 on OEIS to find that it is known to some degree, but expressed differently and not as generally as here - I guess recreational maths peeps think alike :-)
Enjoy. --Paddy3118 (talk) 06:54, 27 April 2019 (UTC)
- It is very well studied, but you must state it slightly differently. Let P2 be the infinite sequence of successive primes (p2_a,P2_b) such that P2_b-P2_a=2. and P4 be the similar infinite sequence (P4_a,P4_b) such that P4_b-P4_a = 4. The your generalization to P2P4 as 3 successive primes with Pa,Pb,Pc with Pb-Pa=2 and Pc-Pb=4 is a search through P2 and P4 to find P2_b=P4_a. An interesting study would be to compute over a large range the length of P2 and P4 and thus predict the length of P2P4. For a given range should the length of P2P4 be the same as P4P2?--Nigel Galloway (talk) 13:28, 27 April 2019 (UTC)
- I was going to add a twin prime task (and cousin prime task, a difference of four), but was somewhat preempted with addition of the sexy prime task (a difference of six), so I dithered a bit. There are other named difference primes such as devil (also called beast), centennial, and millennial primes. However, having a Rosetta Code task just for twin primes would make the code a lot cleaner and simpler, not to mention faster. This would've made the task solutions more easier to compare (and I think more useful for people who wanted a clean and robust code for just concerning the generation of twin primes). Plus it would be easier to find when people are looking for a simple twin prime generator. -- Gerard Schildberger (talk) 21:25, 27 April 2019 (UTC)
- I googled my age, and found it to be highly totient. And I'll never be highly totient. again. Sigh. -- Gerard Schildberger (talk) 21:38, 27 April 2019 (UTC)
Is the first solution for 6,4,2 not 7,13,17,19?--CalmoSoft (talk) 10:40, 7 September 2021 (UTC)
- No, because the next prime after 7 is 11. --Tigerofdarkness (talk) 11:30, 7 September 2021 (UTC)