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.

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 an only prime number which 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:

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139),….

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 present in them are called composite numbers.

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

Problems on Twin Primes

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 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).

Related Links