@peter sorry but i realized that my internet connection doesnt work...i dont know if i can renew my contract...Aaron meyerowitz replied to your post on mathoverflow..i didnt understand well what he says but it seems that primes found are too few for drawing conclusions...i didnt understand what he is saying about bases...it would be interesting to know if there are other primes between k=100.000 and k=200.000 in particular with residue 1...today i will try to renoval my internet contract...

In 10 days i will have internet

@Peter next monday my search up to k=300.000 should have been finished...so the computer of my office is free for other your conjectures...