IJSEA Archive (Volume 6, Issue 12)
International Journal of Science and Engineering Applications (IJSEA) (Volume 6, Issue 12 December 2017)
Symmetry Distribution Law of Prime Numbers on Positive Integers and Related Results
Keywords: similarity distribution; odd primes; congruence theory; Chinese remainder theorem; Fermat's method of infinite descent
This article presents a new theorem concerning the distribution of prime numbers: Let integer n ≥ 4, then there exist two distinct odd primes p and q such that n ﹣p ＝ q ﹣n. The proof of the theorem is established by using the congruence theory and Fermat's method of infinite descent. Moreover, several results are presented to highlight the significance of the theorem.
G. H. Hardy & E. M. Wright. An Introduction to the Theory of Numbers, 5th ed., Oxford science publications, Oxford, Oxford University press, 1980, ⅩⅫThe series of primes (3), 22.3 Bertrand's postulate and a ‘formula’ for primes, P.343.
M. B. Nathanson. Elementary Methods in Number Theory, Springer-Verlag, Beijing, 2003, Section II, Divisors and Primes in Multiplicative Number Theory, 8 Prime Numbers, 8.4, notes3, P.287.
title = " Symmetry Distribution Law of Prime Numbers on Positive Integers and Related Results ",
journal = "International Journal of Science and Engineering Applications (IJSEA)",
volume = "6",
number = "12",
pages = "360 - 363 ",
year = "2017",
author = " Yibing Qiu ",