Geometrical Equivalents of Goldbach Conjecture
There are conjectures and conjectures, here is one of my own, making use of Ackermann functions. The definition of these functions is given by the equations
A(0,n)= mn; A(k,1)= m; A(k,n)=A[k-1,A(k,n-1)].
If we take m=2, we get A(3,4)=2^2^2^...2^2^2, with 65536 two's in it. To get the enormity of this number, compare it with 136x(2^256), the number of electrons in the universe as given by Arthur Eddington. The point we want to make is that A(3,n) grows unimaginably fast with respect to n.
My Conjecture: A(3,n)+1 is a prime for all n.
Compare this with Eermat's disproved conjecture: (2^2^n}+1 is a prime for all n. Note: (2^2^5)+1=641x6700417.
While there is nothing wrong with my conjecture, most mathematicians would keep away from it, perhaps, with the exception of computer scientists who do research on recursive functions. If you are interested in the conjecture anyway, see the exercises at the end of
You do not have to be a mathematician or a computer scientist to understand and appreciate Goldbach Conjecture, which states that every even number greater than 4 can be expressed as the sum of two odd primes. If you like to see a statement of Goldbach Conjecture in terms of geometry, see any of the following:
Geometrical Euivalents of Goldbach Conjecture
Monday, November 12, 2007
