What are Twin Primes?

Two prime numbers are called twin primes if there is present only one composite number between them. Or we can also say two prime numbers whose difference is two are called twin primes. For example, (3,5) are twin primes, since the difference between the two numbers 5 – 3 = 2. The alternative names, given to twin primes are prime twin or prime pair. Also, learn prime numbers here.

Twin Prime Numbers List

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}

Properties of Twin Primes

• (2,3) are not considered as twin primes, since there is no composite number in between them and the difference between the two primes is not equal to 2.
• 5 is the only prime number that is available in two different pairs
• Every prime pair other than (3,5) is in the form of (6n-1, 6n+1), where n is any natural number.
• The sum of each prime pair apart from (3,5) is divisible by 12.

First Few Pairs of Twin Primes

The first fifteen pairs of twin primes are as follows:

Also check:

• Co-Prime Numbers
• Prime Factors

What are Prime Triplets?

A set of three prime numbers which can be represented in the form of (n, n+2, n+6) or (n, n+4, n+6) are called prime triplets.

For example: (5, 7, 11), (7, 11, 13), (11, 13, 17), (13, 17, 19), (17, 19, 23), etc.

Prime Numbers

The numbers which have only two factors, one and the number itself, are called prime numbers.

For example: 2,3,5,7,11,13,17,19, etc. are prime numbers.

Composite Numbers

The numbers which have more than two factors are called composite numbers.

For example: 4,6,8,10,12,14,15, etc. are composite numbers.

Video Lesson

Twin Primes and Co-Primes

Solved Problems

Q.1: Give three pairs of prime numbers whose difference is 2.

Solution: The three pairs of prime numbers are (3, 5), (5, 7) and (11, 13).

Q.2: What is the difference between twin primes and co-prime numbers?

Answer: A pair of prime numbers whose difference is 2, is called twin prime whereas two numbers having only 1 as a common factor is called co-prime numbers.

Q.3: What are the twin primes between 1 and 100?

Answer: The twin primes between 1 and 100 are;

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).