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About an even as the Sum or the Difference of Two Primes

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Abstract:

The present algebraic development begins by an exposition of the data of the problem. The definition of the primal radius r>0 is : For all positive integer x≥3 exists a finite number of integers called the primal radius r>0, for which x+r and x-r are prime numbers. The corollary is that 2x=(x+r)+(x-r) is always the sum of a finite number of primes. Also, for all positive integer x≥0, exists an infinity of integers r>0, for which x+r and r-x are prime numbers. The conclusion is that 2x=(x+r)-(r-x) is always an infinity of differences of primes.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 5)
Pages:
35-43
Citation:
J. Ghanouchi, "About an even as the Sum or the Difference of Two Primes", Bulletin of Mathematical Sciences and Applications, Vol. 5, pp. 35-43, 2013
Online since:
August 2013
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References:

J. R. Chen, 2002, On the representation of a larger even integer as the sum of a prime and the product of at most two primes. Sci. Sinica 16, 157-176.

D. R. Heath-Brown, J. C. Puchta, 2002, Integers represented as a sum of primes and powers of two. The Asian Journal of Mathematics, 6, no. 3, pages 535-565.

H.L. Montgomery, Vaughan, R. C., 1975, The exceptional set in Goldbach's problem. Collection of articles in memory of Jurii Vladimirovich Linnik. Acta Arith. 27, 353-370.

J. Richstein, 2001, Verifying the goldbach conjecture up to 4· 1014, Math. Comp., 70: 236, 1745-1749.

L. E. Dickson, 2005, History of The Theory of Numbers, Vol1, New York Dover.

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