Recent content by kyleballiet

I believe a proof of Legendre -> Andrica may go something like the attachment. Also, if Legendre's Conjecture is proven, it not only guarantees that there's a prime in the interval... it actually gurantees that there are 2 primes satisfying the inequality. This may be easily shown, but I...

Is it possible to find a formula to expand this polynomial: (n+1)(n+2)\ldots(n+x) where n,x\in\textbf{N}. In other words, is it possible to deduce a formula F such that \displaystyle\prod_{k=1}^x{(n+k)}=\displaystyle\sum_{LB}^{UB}F Where LB and UB are the respective lower and upper...

Throw me an E-mail: my user name on here @gmail.com and I'll be happy to send a pre-print to you.

It's interesting to note that Chebyshev was the first to show Bertrand in 1850, and Erdos stated it elementarily in 1932 although it wasn't until 2006 when Bachraoui showed [2n, 3n]. Another interesting thing is that Erdos checked the values for n = 1, 2, ..., 96, and Bachraoui had to check...

Bertrand's Postulate states: For n > 1, there is a prime p satisfying n < p < 2n. M. El Bachraoui proved in 2006: For n > 2, there is always a prime p satisfying 2n < p < 3n. In general, if you were to prove: For all n >= k >= 1, there is always a prime p satisfying kn < p < (k+1)n, then...