The Polygnac conjecture was a strong conjecture belonging to twin prime numbers. For all natural numbers k, there were infinitely many prime pairs (p, p + 2k). The case of k=1 was the twin prime number conjecture where there were infinite prime numbers p such that p+2 was a prime number.
The latter was already proved by Lu Zhou, using a topology method.
Prior to this, Zhang Yitang and other mathematicians had completed the proof for "bounded distance between prime numbers" from 70 million to 246. These conclusions all belonged to the (P, P+2K) form, which also provided a powerful clue for the proof of the Polignac conjecture.
So far, "…", "k=123, "k=…" etc had been completed.
However, the last step, k=1, was still unproven.
If the twin prime conjecture gave Lu Zhou a nomination for the Fields Medal, then the proof of the Polignac's conjecture would guarantee his win.
However, to prove that K=all natural numbers were true was not an easy task.
