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: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=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>''.
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Note that the integer ''R<sub>n</sub>'' is necessarily a prime number: <math>\pi(x) - \pi(x/2)</math> and, hence, <math>\pi(x)</math> must increase by obtaining another prime at ''x'' = ''R<sub>n</sub>''. Since <math>\pi(x) - \pi(x/2)</math> can increase by at most 1,
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