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what is the Best known Upper bound on Twin Primes?

Has someone proven a lower bound on the number of primes less than or equal to x that are congruent to 1(mod3)?

  • I know the approximation that has been proven of this from Dirichlet's theorem, but I am interested in a lower bound provided that x is greater than a certain value. For example, has someone proved something like the number of primes less than or equal to x that are congruent to 1(mod3) is always greater than 0.495*PI(x) when x>1,000,000?

  • Answer:

    This may be of some help, http://www.math.ubc.ca/~gerg/slides/chennai The densities of primes in various congruence classes amodn are found to have an edge when a is not a quadratic residue modn. For example, p=1mod3 is not so numerous as p=2mod3.

Nathan G at Yahoo! Answers Visit the source

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