@Peter k=300.000 accomplished!

Nobody has tried to find a prime with other residue in the range 100.000-200.000

So, no prime upto 300k! In fact a milestone.

@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

I could post the candidates in the ranges 100 000-110 000 , 110 000 to 120 000 and so on. The whole range will probably contain too many candidates.

@Peter Ok thanks

@Peter have you continued to test your conjecture $f(n)/5$?

No, I haven't, maybe I continue the search a bit.

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 ?

@Peter if you want yes...

I have posted the 1398 candidates in the range 100 000 to 110 000 on github.