There are infinitely many primes p such that p + 2 is also prime.
First off, I'm a noob at maths and always reverse my logic!
Now, a little glimpse into my madness.
I saw this unsolved twin prime conjecture several days ago and tried to solve it. After 15 mins I constructed the above visual proof.
Here's how I thought it should work: Let line P represent the Infinitude of Primes. To be a member of P, the number must be prime. All other numbers are excluded. Next, pick a prime p and draw a 2D lattice L with sides sqrt(2). Notice how P is the on the lattice diagonal.
At this stage, I knew at least one lattice square would intersect P at two distinct primes, say p and p+2 (if it exists!?). Now to prove that p+2 exists, I decided to use Polya's 2D random walk which proves that any point is reachable on a 2D lattice. I intentionally allowed the lattice point to represent p+2. So, let the random walk (shown in red) proceed and eventually it'll reach the lattice prime point p+2. Thus, if it's possible to reach p+2 from p, then p+2 must exist and is prime since it lies on P. Q.E.D.
Okay, where did I go wrong?