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In https://arxiv.org/abs/1009.3956 is it shown there is a $c>0$ such that $\pi(x)\bmod2$ can be computed in $o(x^{\frac12})$ time (more precisely number of primes $\bmod 2$ for an interval of length at most $O(x^{\frac12+c})$ in $[x,2x]$ can be computed in time $O(x^{\frac12-c})$)?

If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

We know that Cramer's conjecture detects primes in $[x,2x]$ in $P$.

Assuming Cramer's or Riemann's conjecture is $\frac12-c=o(1)$ believed achievable for $\pi(x)\bmod2$?

In https://arxiv.org/abs/1009.3956 is it shown there is a $c>0$ such that $\pi(x)\bmod2$ can be computed in $o(x^{\frac12})$ time (more precisely number of primes $\bmod 2$ for an interval of length at most $O(x^{\frac12+c})$ in $[x,2x]$ can be computed in time $O(x^{\frac12-c})$)?

If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

In https://arxiv.org/abs/1009.3956 is it shown there is a $c>0$ such that $\pi(x)\bmod2$ can be computed in $o(x^{\frac12})$ time (more precisely number of primes $\bmod 2$ for an interval of length at most $O(x^{\frac12+c})$ in $[x,2x]$ can be computed in time $O(x^{\frac12-c})$)?

If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

We know that Cramer's conjecture detects primes in $[x,2x]$ in $P$.

Assuming Cramer's or Riemann's conjecture is $\frac12-c=o(1)$ believed achievable for $\pi(x)\bmod2$?

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In https://arxiv.org/abs/1009.3956 is it shown there is a $c>0$ such that $\pi(x)\bmod2$ can be computed in $o(x^{\frac12})$ time (more precisely number of primes $\bmod 2$ for an interval of length at most $O(x^{\frac12+c})$ in $[x,2x]$ can be computed in time $O(x^{\frac12-c})$)?

  1. If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

  2. Is the technique applicable to union of disjoint intervals without testing them separately?

If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

In https://arxiv.org/abs/1009.3956 is it shown there is a $c>0$ such that $\pi(x)\bmod2$ can be computed in $o(x^{\frac12})$ time (more precisely number of primes $\bmod 2$ for an interval of length at most $O(x^{\frac12+c})$ in $[x,2x]$ can be computed in time $O(x^{\frac12-c})$)?

  1. If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

  2. Is the technique applicable to union of disjoint intervals without testing them separately?

In https://arxiv.org/abs/1009.3956 is it shown there is a $c>0$ such that $\pi(x)\bmod2$ can be computed in $o(x^{\frac12})$ time (more precisely number of primes $\bmod 2$ for an interval of length at most $O(x^{\frac12+c})$ in $[x,2x]$ can be computed in time $O(x^{\frac12-c})$)?

If so is there a good estimate known for $c$ and is $\frac12-c=o(1)$ believed achievable?

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