Ramanujan prime: Difference between revisions

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Line 13: The converse of this result is the definition of Ramanujan primes: :The ''n''th Ramanujan prime is the least integer ''R<sub>n</sub>'' for which <math>\pi(x) - \pi(x/2) \ge n,</math> for all ''x'' ≥ ''R<sub>n</sub>''.<ref>{{MathWorld\|~~\|authorlink~~author-link=Jonathan Sondow\|author=Jonathan Sondow\|title=Ramanujan Prime\|urlname=RamanujanPrime}}</ref> In other words: Ramanujan primes are the least integers ''R<sub>n</sub>'' for which there are at least ''n'' primes between ''x'' and ''x''/2 for all ''x'' ≥ ''R<sub>n</sub>''. The first five Ramanujan primes are thus 2, 11, 17, 29, and 41.