A Question to Trouble Even the Best of You

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.

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.

DaveC426913

What is an "arithmetical sequence"?

Data

An arithmetic sequence is one of the form [itex](n,n+k,n+2k,n+3k,...,n+mk,...)[/itex].

tehno

Ah,yes,yes,...
To me it makes sense to start with 199 and find "minimum" prime-sequence of 10 terms with spacing 210 :

[tex]
199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 [/tex].

But it took me longer time ,about 10 seconds

Edgardo

I've written a mini-introduction to arithmetic progressions here

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

d_leet

51 and 81 are both composite.

mr200backstrok

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)

Data

All I used for this problem was a little bit of modular arithmetic.