bertrand'stheorem

Bertrand's Theorem

For all n, there exists a prime p, s.t. n<=p<2n

Proof:

Either: For all n, there exists m s.t. prime, p = n+m, with: 0<=m<n

Or: For all m, there exists n s.t. prime, p = m+n, with: 0<=n<m

Therefore

Either: n<=p<2n

Or: m<=p<2m

From which result follows

Copyright 1998 James Wanless