
Re: Vindication of Goldbach's conjecture
Posted:
Jun 22, 2012 9:21 AM


On 22/06/2012 13:58, mluttgens wrote:
>>> Hereafter are the numbers n of Goldbach's sums for increasing even >>> numbers N: >> >>> N n >>> _ _ >> >>> 50 8 >>> 100 12 >>> 500 26 >>> 1000 56 >>> 5000 152 >>> 10000 254 >>> 50000 900 >>> 100000 1628 >> >>> Clearly, when N increases, the number of Goldbach's sums also >>> increases. >> >> Except when it doesn't: >> >> 450000 11028 >> 455000 7526 >> 460000 5840 > > How did you find those numbers? What do they represent? > If 11028, 7526 and 5840 represent Goldbach's pairs, they are false.
There are 11028 ordered pairs of primes (p,q) with p + q = 450000. There are 7526 ordered pairs of primes (p,q) with p + q = 455000. There are 5840 ordered pairs of primes (p,q) with p + q = 460000. (I could list them, but I think I will spare the readers of sci.math).
There is an error above: there are 1620 ordered pairs of primes (p,q) with p + q = 100000 (not 1628 of them).

