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:
| (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), … |
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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).
Frequently Asked Questions on Twin Prime Numbers
What are twin prime numbers?
Two prime numbers are called twin prime numbers if they have only one composite number between them. In simple words, two prime numbers whose difference is 2 are called twin primes.
What are the example of twin prime numbers?
Two examples of twin prime numbers are:
(3, 5); here 3, 5 are prime numbers and 4 is the composite number between them.
(5, 7); here 5, 7 are prime numbers and 6 is the composite number between them.
Are 43 and 47 twin primes?
No, 43 and 47 are not twin prime numbers since the difference between these two numbers is not equal to 2.
Why 11 and 13 is twin prime pair?
11 and 13 is a twin prime pair since 11 and 13 are two prime numbers that has only one composite number between them, i.e. 12. Also, the difference between these two numbers is 2.
How many twin prime numbers are there between 1 and 50?
There are six twin prime numbers pairs between 1 and 50; they are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), and (41, 43).