For n 1, the nth Ramanujan prime is defined as the least positive integer Rn such that for all x Rn, the interval ( x 2 , x] has at least n primes. If ? = 2n 1 + 3 log n + log2 n 4 , then we show that Rn < p[?] for all n > 241, where pi is the i th prime. This bound improves upon all previous bounds for large n.
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机译：对于n 1，第n个ramanujan素数被定义为最小的整数Rn，使得对于所有x rn，间隔（x 2，x]具有至少n个次电压。如果？= 2n 1 + 3 log n + log2 n 4然后，我们向所有N> 241显示RN
