Hi,
I am offering a math prize that starts as of the posting of this message and will expire in two weeks time.
The prize is potentially the largest prize in math ever offered, and also potentially the smallest math prize ever offered.
The prize scales with the solution found which means that extra computation time will potentially produce a more valuable solution.
The prize is $1 for every link in a Goldbach chain that you can find beyond 5 links.
With a modest search I already several examples of Goldbach chains with
5 links, so if you find a chain with 100 links that is a $95 prize.
I am not sure if the maximum Goldbach chain length is finite or infinite either, so as you can see there is no upper bound to the prize, at $1 per link.
Ok so if you don't know what a Goldbach chain is, here are five examples of length=5 Goldbach chains:
37,210,383-383,420,457-457,840,1223-1223,1680,2137-2137,3360,4583
137,210,283-283,420,557-557,840,1123-1123,1680,2237-2237,3360,4483
197,210,223-223,420,617-617,840,1063-1063,1680,2297-2297,3360,4423
7,30,53-53,60,67-67,120,173-173,240,307-307,480,653
13,30,47-47,60,73-73,120,167-167,240,313-313,480,647
They have the pattern a1,b1,c1-a2,b2,c2-a3,b3,c3-a4,b4,c4-a5,b5,c5
The Goldbach chains have all these properties:
a and c are prime
b-a are prime
c-b are prime
b can be any number you choose
b(n)=b(n+1)/2
b(n)=b(n-1)*2
c-b=b-a
c(n)-b(n) = a(n-1)
(c-b)+a=b
Good luck!!!!
cheers, Jamie