A prime number is a number that cannot be divided by other numbers than itself and the number 1. Here is a list of the prime numbers below one hundred: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Two consecutive prime numbers are called twin primes if their difference is equal to two. If you have a look at the list of prime numbers above, you will realize that the first pairs of twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), and (71, 73).
Since the great Euclid, §11, (around 300 BC) we know that there are infinitely many prime numbers. But, are there infinitely many twin primes?
Mathematicians believe that the answer is yes, but nobody has been able to prove this conjecture yet.
Note that the only even prime is 2, so twin primes are as closely spaced as possible for two primes —with a gap distance of 2—, except for the pair (2, 3) with a gap distance of 1. In April 2013, Yitang Zhang announced the discovery that there are infinitely many pairs of primes that differ by a gap of some number below approximately 70,000,000. Two years later, in 2015, James Maynard and his group showed that there are infinitely many pairs of primes that differ by at most 246. This number is quite closer to the number 2 of the twin primes conjecture than the first result involving the number 70,000,000. The conjecture about twin primes is likely to become a theorem soon! (We hope). Nowadays, the math community is trying to reduce this large gap of 246 to just 2 units.