No, this is absolutely <i>not</i> the first (correct) proof that infinitely many prime numbers come in pairs! That is the twin prime conjecture, and at the time of writing this comment, steadily remains a conjecture. I wonder why <i>Nature</i>, a publication held in high regard, would publish an article with such a title. This is not to say that the result is anything less than incredible.<p>Terence Tao delivered a very good lecture on this result here [0]<p>[0] <a href="https://www.youtube.com/watch?v=pp06oGD4m00" rel="nofollow">https://www.youtube.com/watch?v=pp06oGD4m00</a>