@Peter When I will have my internet connection at home I would try to search for primes with other residue than 6 in the range 100.000-250.000...the residues 1 mod 7 seems to appear twice than expected but I think that it will be difficult to find other such primes
Even in the range 100 000-110 000 , I have still 1514 candidates left. I can slightly decrease this number with further sieving, but I do not think that I can get below 1000. So, the search will become painful. Should I post the candidates ?