What is the lowest arithmetic sequence of positive prime integers that has 3 terms? 5 terms? 8 terms?

What is the constant difference for the lowest N positive prime integers in arithmetic sequence?

What would the first term be for such a sequence?

(A prime sequence is "lowest" if the average of its terms is the lowest. If any are tied then it is the one with the smallest starting term.)

(In reply to Partial solution by K Sengupta)

3, 5, 7 is in arithmetic sequence and, by the problem's definition, is the lowest such sequence of 3 positive prime integers.

Did not see Gamer's subsequent change to the problem definition until after writing the above. So, in the light of the problem, change, yes, {5, 11, 17} is the lowest 3 term sequence.

(I thought it was too easy - especially for a skilled number theorist like KS!!!)

 

Edited on May 16, 2007, 5:51 pm

Posted by JayDeeKay on 2007-05-16 17:40:06