JP Journal of Algebra, Number Theory and Applications
Volume 18, Issue 2, Pages 145 - 164
(September 2010)
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A NEW VIEW OF THE NATURAL NUMBER SET N
Bao Qi Feng, Louis Feng and Dong Ning Zhao
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Abstract: In 1981, Pritchard [1, 2] created remarkably a new sieve for finding all prime numbers in the natural number set N. In this paper, we give a new instruction of N, from which we can see a new view of the distribution of prime numbers in the set N. We also give a strictly mathematical proof for the Pritchard’s sieve for offering it a solid mathematical support. Finally, we give new proofs for the infinitude and the asymptotic density formula of the primes number set P in the natural number set N, respectively. |
Keywords and phrases: arithmetic progression, asymptotic density, composite number, least prime factor, prime number, sieve, Eratosthenes’ sieve. |
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