Quote:
Originally Posted by Dobri
π_{3,2}(2) = π_{3,1}(2) = 0 (trivial case)
π_{3,2}(3) = π_{3,1}(3) = 0 (trivial case)
π_{3,2}(7) = π_{3,1}(7) = 1
...

Don't forget 2 is a prime of the form 2 mod 3.
Quote:
Originally Posted by Dobri
Indeed, it is unclear (at least to me) what happens at x > Infinity.
It could be π_{3,2}(x) = π_{3,1}(x) + C for some small nonzero constant C. Or C=0?

Littlewood's result from 1914, quoted in Granville and Martin's survey, shows that the difference oscillates from positive to negative infinitely many times, and also takes arbitrarily large positive and negative values.