1 6 N ov 1 99 8 On the nonasymptotic prime number distribution ∗
نویسنده
چکیده
The objective of this paper is to introduce an approach to the study of the nonasymptotic distribution of prime numbers. The natural numbers are represented by theorem 1 in the matrix form N . The first column of the infinite matrix N starts with the unit and contains all composite numbers in ascending order. The infinite rows of this matrix except for the first elements contain prime numbers only, which are determined by an uniform recurrence law. At least one of the elements of the twin pairs of prime numbers is an element of the second column of the matrix N (theorem 3). The basic information on the nonasymptotic prime number distribution is contained in the distribution of the elements of the second column of the matrix N .
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Let σ(n) denote the sum of positive divisors of the natural number n. Such a number is said to be perfect if σ(n) = 2n. It is well known that a number is even and perfect if and only if it has the form 2p−1(2p − 1) where 2p − 1 is prime. It is unknown whether or not odd perfect numbers exist, although many conditions necessary for their existence have been found. For example, Cohen and Hagis ha...
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تاریخ انتشار 1998