In an earlier post, I explained what prime numbers are and how to find them using a sieve. In this post, I will tell you a little about twin primes.

Twin primes are pairs of prime numbers separated by a non-prime (composite) number. So, using our sieve (shown below with prime numbers highlighted, and twin primes in red with darker yellow highlighting), we can see that the twin primes up to 100 are:

3, 5

5, 7

11, 13

17, 19

29, 31

41, 43

59, 61

71, 73

The twin prime conjecture states that there are an infinite number of these pairs. This proposition is called a conjecture because it has not been proven. This video from Nova, says that the twin prime conjecture was proposed by Euclid, but it seems that some believe it was actually first proposed by Alphonse de Polignac.