The Generalized G oldbach’s Conjecture:Symmetry of Prime · PDF fileThe Generalized Goldbach’s Conjecture: Symmetry. of Prime Number Jian Ye . Keywords: the generalized...
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Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 14 Issue 7 Version 1.0 Year 2014 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896
By Jian Ye Sichuan University, China
Abstract- Goldbach’s conjecture: symmetrical primes exists in natural numbers. the generalized Goldbach's conjecture: symmetry of prime number in the former and tolerance coprime to arithmetic progression still exists.
Keywords: the generalized goldbach's conjecture, symmetry of prime number.
GJSFR-F Classification : FOR Code : MSC 2010: 11B25. 11N13
Author: Sichuan University College of Mathematics, Chengdu 610207, China. e-mail: [email protected]
Abstract- Goldbach's conjecture: symmetrical primes exists in natural numbers. the generalized Goldbach's conjecture: symmetry of prime number in the former and tolerance coprime to arithmetic progression still exists.
PPPPp a prime number.a: a constant number,O: mean big O notation describes the limiting behavior of a function when theargument tends towards a particular value or infinity, usually in terms of simplerfunctions.p|k: p dividesk.
φ(q): φ(q) Euler phi-function.: express the logarithmic integral function or integral logarithm. is
special function such as
ssquequesum of two primestwo primes. G( ) the number of representatives a large even integer x :
:a >0
is the
.
x sum of as a
sum of two primesG(x, q, L) : the number of representatives a large even integerssquequesum of two primes two primes
x as a
arithmetic .progression in the former L and tolerance q coprime tosum
Li (x)2Li (x)
2∫ x
2dt
ln t.2Li (x)
2 =a
of
sum of two primes
In the former L and tolerance q (L < q, q ≥ 2) coprime to arithmeticfor any one item of this progression such as x
2where x
2 > φ(q) ·q 2
for a sum of two primes in its series.
Let G(x, q, L) is the number of representatives a large even integerssquequesum of two primes two primes
,
x as a
symmetrical primes onleast a pair of x2
, namely xeven integer can
arithmetic .progression in the former L and tolerance q coprime to