[Guest]

Does there exist a set of 11 distinct primes, with each of the primes being less than 20000, such that the foregoing set of primes corresponds to 11 consecutive terms of an arithmetic progression in ascending order of magnitude?

If the answer to the above query is in the affirmative, give an example. Otherwise, prove that such a set of primes, in conformity with the given conditions, cannot exist.

Edited October 24, 2009 by K Sengupta

[superprismatic]

No, it is easy enough to exhaust over all possible arithmetic sequences with a program. The longest such sequence for primes less than 20000 is the 10-long arithmetic sequence 199,409,619,829,1039,1249,1459,1669,1879,2089.

So, proof here is by exhaustion.

[bushindo]

Those who are intrigued by this problem may be interested in this theorem

Green–Tao theorem