Related to other recent posts here by me, I wish to point out another problem that might be doable with adequate software and hardware but not by me soon. A172994 (

http://oeis.org/A172994 ) has only 4 terms and so has attribute 'more' attached to it. The 6th term is 66 and all later ones (by any reasonable expectation) are 2.

What's needed is the first positive integer n for which 8 (at least) of the values {n^(2i)+n^i-1: 0<i<13} are prime. If anybody wants to try it... please do.

The 7th and many later terms are positively evaluated as 2, and the contrary of the stated expectation is essentially equivalent to a (much) biased random walk on the line already far in the direction of bias returning to the origin.

A couple of odd notes: A) I suspect the 9th value for 66 being at i=22 may in some sense be the most extreme specific small-number coincidence in this general question, and the 10th and 11th are at 77 and 690 (without another known); and B) The large value of the 4th term in the sequence coincidentally manages another prime already (8th after the 7th at i=9) with i=37.

JGM