Hi Bruno,

p+1 would not be prime. Isn't p+2 the smallest except for 2,3. I do use Euclid's theorem that there are an infinite number of primes.

Think of it this way ... "line" P is simply a representation of a prime boundary P={2,3,5,7,11,13,...}, so that superimposing a 2D grid will cross that boundary at two prime points, p and p+2 (if it exists?)

The primary goal is to prove that p+2 exists. I tried to prove p+2 exists by finding a path from point p to p+2 by using a random walk by Polya.

The key "trick" is to align prime p and a lattice point to create a "prime lattice point" p+2 so that I could say p+2 is prime (since it lies on P) and also simultaneously state that p+2 exists as it's a lattice point.

Combining them together, p+2 is prime and exists!

Perhaps my proof is flawed by a construction argument?

Thanks for the reply.