On Small Intervals Containing Primes
نویسنده
چکیده
Let p be an odd prime, such that pn < p/2 < pn+1, where pn is the n-th prime. We study the following question: with what probability does there exist a prime in the interval (p, 2pn+1)? After the strong definition of the probability with help of the Ramanujan primes ([11], [12])and the introducing pseudo-Ramanujan primes, we show, that if such probability P exists, then P ≥ 0.5. We also study a symmetrical case of the left intervals, which connected with sequence A080359 in [10].
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