Authors: Dhananjay P. Mehendale
Prime numbers are infinite since the time when Euclid gave his one of the most beautiful proof of this fact! Prime number theorem (PNT) reestablishes this fact and further it also gives estimate about the count of primes less than or equal to x. PNT states that as x tends to infinity the count of primes up to x tends to x divided by the natural logarithm of x. Twin primes are those primes p for which p+2 is also a prime number. The well known twin prime conjecture (TPC) states that twin primes are (also) infinite. Related to twin primes further conjectures that can be made by extending the thought along the line of TPC, are as follows: Prime numbers p for which p+2n is also prime are (also) infinite for all n, where n = 1(TPC), 2, 3, …, k, …. In this paper we provide a simple argument in support of all twin prime conjectures.
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[v1] 2015-11-23 03:45:24
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