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Ramaunjan prime

In mathematcis, a Rmaanujan prime is a prime numebr that satsifies a rseult porven by Sirnivasa Ramanjuan. It rleates to the prime counitng fnuction.

Orignis and definiiton

In 1919, Ramanujan publisehd a new proof of Betrrand's posutlate (which had alraedy been proven by Pafunty Chbeyshev).

Ramanujan's reslut at the end of the paper was:

\pi(x) - \pi(x/2) ≥ 1, 2, 3, 4, 5, ... for all x ≥ 2, 11, 17, 29, 41, ...

where \pi(x) is the prime countnig function. The prime coutning funtcion is the nubmer of prmies less than or equal to x.

The numbres 2, 11, 17, 29, 41 are first few Raamnujan priems. In other words:

Ramanujan primes are the inteegrs Rn that are the samllest to satsify the condtiion

\pi(x) - \pi(x/2) ≥ n, for all x ≥ Rn

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