About an even as the sum or the difference of two primes

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Ghannouchi , Jamel (2013)
  • Publisher: HAL CCSD
  • Subject: 11D04 | Goldbach | Algebraic proof | [ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM] | Twin primes | De Polignac
    arxiv: Mathematics::Number Theory

13 pages; International audience; The present algebraic development begins by an exposition of the data of the problem. The definition of the primal radius is : For all positive integer exists a finite number of integers called the primal radius , for which and are prime numbers. The corollary is that is always the sum of a finite number of primes. Also, for all positive integer , exists an infinity of integers , for which and are prime numbers. The conclusion is that is always an infinity of differences of primes.
  • References (3)

    [1] Van der Corput, J. G. "Sur l'hypothese de Goldbach" Proc. Akad. Wet. Amsterdam , 41, 76-80 (1938).

    [2] Estermann, T. "On Goldbach's problem : proof that almost all even positive integers are sums of two primes" Proc. London Math. Soc. 2 44, 307-314 (1938).

    [3] Sinisalo, Matti K. "Checking the Goldbach Conjecture up to 4 1011" Mathematics of Computation 61, 931-934 (1993).

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