quasi
Posts:
12,042
Registered:
7/15/05


Re: Vindication of Goldbach's conjecture
Posted:
Jun 17, 2012 2:17 PM


On Sun, 17 Jun 2012 02:20:49 0700 (PDT), mluttgens <luttgma@gmail.com> wrote:
>83749105938571693046 = 157 + 83749105938571692889 > = 277 + 83749105938571692769 > = 283 + 83749105938571692763 > = 487 + 83749105938571692559 >etc... etc... etc...
Notice that 157 is the _smallest_ prime that works.
Thus, the following attempts all fail:
83749105938571693046 = 3 + 83749105938571693043 5 + 83749105938571693041 7 + 83749105938571693039 11 + 83749105938571693035 13 + 83749105938571693033 17 + 83749105938571693029 ... 151 + 83749105938571692895
So by trial and error, you find that 157 works, but you didn't know that before you checked the other summand. So how did you know in advance that some prime was going to work?
To prove Goldbach's Conjecture, you have to show, for the general even n > 4, not a just a particular case, that a pair of odd primes exists whose sum is n. That you haven't done.
Note: "mutatis mutandi" is not a valid principle of mathematical reasoning.
quasi

