On the Goldbach-Euler Theorem concerning Primes

Article metrics


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.