primes mod 3

[Joshua Zucker]

Up to 10^8, at least according to my program, once 2 gets the lead in
the camp of "primes = 2 mod 3", there are always more primes = 2 mod 3
between 1 and n than there are primes = 1 mod 3.

Does anyone have a reference about some future crossing point, where
the primes = 1 mod 3 catch up?  My data say that 233 is the last time
it gets really close, 1889 is the last time it's within 2, and 198593
is the last time that it's within 3 (again, searching up to 10^8).

Thanks,
--Joshua Zucker