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 2*x*=(*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 2*x*=(*x+r*)-(*r-x*) is always an infinity of differences of primes.

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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Distribution:

Open Access

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Creative Commons Attribution 4.0 International License

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.