Twin Prime Numbers are the set of two numbers that have exactly one composite number between them. They can also be defined as the pair of numbers with a difference of 2. The name twin Prime was coined by Stackel in 1916. In simple words, we can say that where two numbers have a difference of 2, they are said to be Twin Primes. The word twin prime is also used to describe one of the twin primes i.e. twin prime is a prime with a prime gap of 2.
Properties of Twin-Prime Numbers:
We know that twin primes are pairs of prime numbers with a difference of two. There are few basic properties for twin primes. Let us discuss the properties of twin primes in detail:
- 5 is the only prime number that has a positive as well as a negative prime gap of two and hence is the only prime to occur in two twin primes pair.
- Every twin primes pair other than {3, 5} is of the form {6n-1, 6n+1}
- Pair of numbers is not considered a twin prime, if there is no composite number between them, for example, {2, 3} can not be considered a twin prime pair. as there is no composite number between them.
- The sum of each twin prime pair except {3,5} is divisible by 12 as (6n-1) + (6n+1) = 12n.
The list of twin prime numbers from 1 to 1000 are given here:
Twin prime numbers from 1 to 50
{3, 5}, {5, 7}, {11, 13}, {17, 19}, {29, 31}, {41, 43}
Twin prime numbers from 51 to 100
{59, 61}, {71, 73}
Twin prime numbers from 101 to 200
{101, 103}, {107, 109}, {137, 139}, {149, 151}, {179, 181}, {191, 193}, {197, 199}
Twin prime numbers from 201 to 300
{227, 229}, {239, 241}, {269, 271}, {281, 283}
Twin prime numbers from 301 to 400
{311, 313}, {347, 349}
Twin prime numbers from 401 to 500
{419, 421}, {431, 433}, {461, 463}
Twin prime numbers from 501 to 1000
{521, 523}, {569, 571}, {599, 601}, {617, 619}, {641, 643}, {659, 661}, {809, 811}, {821, 823}, {827, 829}, {857, 859}, {881, 883}
