Unsolved Problems of Primes!

Prime numbers are one of the most basic topics of study in the branch of mathematics called number theory. There are many unanswered questions in Number Theory. Let’s examine some of these.

A conjecture is a statement that has no proof. Generally, for a conjecture, our intuition tells us that the statement is true but we cannot find proof.

1. Twin Prime Conjecture (Euclid around 300BC.)

Twin primes are of the form p and p+2 where p is prime.

Primes like 11 and 13 are examples of twin primes. Other examples are 17 and 19, 41 and 43, 627 and 629, 1 000 000 000 061 and 1 000 000 000 063. The twin prime conjecture of Number theory is:

Conjecture: There are infinitely many primes of the form p and p+2 .

No one has yet come up with proof of this result although most mathematicians do seem to believe it is true. As the numbers get larger, the primes become less frequent and twin primes are very rare. The conjecture is sometimes called Euclid’s Twin Prime conjecture. Euclid gave the oldest known proof that there are infinitely many primes, the link to it is below, but he did not prove the statement about twin primes.