how to prove the infinitude of twin primes?
Answers
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair.
Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown if there are infinitely many twin primes or if there is a largest pair. The work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present it remains unsolved
Well this theorem does not stand true as per my thinking because I strongly believe that the number line is curved which implies that the numbers are finite. The purpose of my believing so is the geometry of the universe which is elliptical (spherical) geometry which implies that nothing in this universe is straight. Every straight line is a part of a circle with infinite circumference. And this straightaway disproves the infinitude of twin primes, polignac's conjecture and other such theorems.