0
$\begingroup$

With two consecutive primes $p_n$ and $ p_{n+1}$ how many solutions does the inequality $$\frac {p_{n+1}-p_n}{2}\ge\pi(p_n) $$ have with $\pi(n) $ being the prime counting function

$\endgroup$
2
$\begingroup$

By Bertrand's postulate (which has been proven, so it's actually more a theorem than a postulate) there is a prime between $n$ and $2n$, so the left hand side of your inequality is less than $\frac{p_n}{2}$, so what your asking comes down to whether more than half the numbers less than $p_n$ are prime. It shouldn't take you long to find all solutions to that question.

$\endgroup$
  • $\begingroup$ so I need to calculate it? $\endgroup$ – Guacho Perez Jun 13 '15 at 12:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.