On the Goldbach-Euler Theorem concerning Primes

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Abstract

I HAVE verified the new law for all the even numbers from 2 to 1000, but will not encumber the pages of NATURE with the retails. The approximate formula hazarded for the number of resolutions of 2n into two primes, viz. , where μ is the number of mid-primes, does not always come near to the true value. I have reasons for thinking that when n is sufficiently great, may possibly be an inferior limit. The generating function given in a recent number of NATURE, p. 196, is subject to a singular correction when the partible number 2n is the double of a prime. In this case, since the development to be squared is the coefficient of x2n will contain 2μ, arising from the combination of 0 with 2n, which is foreign to the question, and accordingly the result given by the generating function would be too great by 2μ.

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SYLVESTER, J. On the Goldbach-Euler Theorem concerning Primes. Nature 55, 269 (1897) doi:10.1038/055269a0

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