Indexed on: 28 Mar '06Published on: 28 Mar '06Published in: Mathematics - General Mathematics
In this paper we use the connected sum operation on knots to show that there is a one-to-one relation between knots and numbers. In this relation prime knots are bijectively assigned with prime numbers such that the prime number 2 corresponds to the trefoil knot. From this relation we have a classification table of knots where knots are one-to-one assigned with numbers. Further this assignment for the $n$th induction step of the number $2^n$ is determined by this assignment for the previous $n-1$ steps. From this induction of assigning knots with numbers we can solve some problems in number theory such as the Goldbach Conjecture and the Twin Prime Conjecture.