## A Question to Trouble Even the Best of You

About five seconds . It makes sense to start at 7; if you can find a sequence starting with 7 that has spacing smaller than 210 (and there's no smaller sequence starting with 7), then that's obviously the smallest one.

Of course, from what I've done there was no particular reason to confine myself to sequences starting with 7, so it would be fair to consider it a lucky coincidence.

 What is an "arithmetical sequence"?
 An arithmetic sequence is one of the form $(n,n+k,n+2k,n+3k,...,n+mk,...)$.

 Quote by Data About five seconds . It makes sense to start at 7; if you can find a sequence starting with 7 that has spacing smaller than 210 (and there's no smaller sequence starting with 7), then that's obviously the smallest one.
Ah,yes,yes,...
To me it makes sense to start with 199 and find "minimum" prime-sequence of 10 terms with spacing 210 :

$$199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089$$.

But it took me longer time ,about 10 seconds

Blog Entries: 2
 Quote by DaveC426913 What is an "arithmetical sequence"?
I've written a mini-introduction to arithmetic progressions here

 what about 31,41,51,61,71,81,91 ? are there any non-primes in there? but even if that is right (i doubt it is, i'm too tired to see the factors i probably should) i cheated b/c i guessed

 Quote by mr200backstrok what about 31,41,51,61,71,81,91 ? are there any non-primes in there? but even if that is right (i doubt it is, i'm too tired to see the factors i probably should) i cheated b/c i guessed
51 and 81 are both composite.

 oh haha 9*9 = 81 yep im tired Any idea where i could get a description of the concepts they are talking about? (I don't want to hijack the thread)

 Quote by mr200backstrok Any idea where i could get a description of the concepts they are talking about? (I don't want to hijack the thread)
All I used for this problem was a little bit of modular arithmetic.