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Old 2021-08-26, 19:37   #11
charybdis
 
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Quote:
Originally Posted by Dobri View Post
π3,2(2) = π3,1(2) = 0 (trivial case)
π3,2(3) = π3,1(3) = 0 (trivial case)
π3,2(7) = π3,1(7) = 1
...
Don't forget 2 is a prime of the form 2 mod 3.

Quote:
Originally Posted by Dobri View Post
Indeed, it is unclear (at least to me) what happens at x -> Infinity.
It could be π3,2(x) = π3,1(x) + C for some small non-zero 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.
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