List all the twin primes between 1 and 50.
List five composite numbers less than 50.
Give five examples of co-primes.
Answers
★ Answer ★
Let's understand the concept first .
★ What are twin prime numbers ?
- Twin primes are pairs of primes of the type (n, n+2).
- Twin primes are two natural numbers the distance between is 2, and which are both prime numbers! {(n,m):n,m∈Prime; m = n+2; m>n }.
Example - { ( 3 ,5 ) , ( 5, 7 ) ······· }
So , Therefore ,
Twin primes between 1 and 50
- ( 2 , 3 )
- ( 5 , 7 )
- ( 11 , 13 )
- ( 17 , 19 )
- ( 29 , 31 )
- ( 41 43)
★ Composite Numbers ★
All the natural numbers except the prime numbers are called composite Numbers.
Examples :- { 4 , 6 , 8 , 10 ········ }
Hence ,
Five composite numbers less than 50.
- 4
- 6
- 8
- 9
- 10
Other composite Numbers less than 50 are - 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49.
★ Co - prime numbers ★
Two numbers are coprime if their highest common factor (or greatest common divisor) is 1.
For example - { (2,3), (5,11), (19,23)········ }
Five examples of co-primes
- ( 2 , 3 )
- ( 5 , 7 )
- ( 11 , 13 )
- ( 17 , 19 )
- ( 29 , 31 )
- ( 41 43)
Other Numbers are :-
★ Even Number ★
The number which are divisible by 2 are called even numbers .
Examples :- { 2 , 4 , 6 , 8 , ········ }
★ Odd Numbers ★
The numbers which are not divisble by 2 are called odd numbers .
Examples :- { 3 , 5 , 7 , 9 , ········ }
★ Prime Numbers ★
The number which are divisible by 1 or itself are called prime numbers.
Examples :- { 2 , 3 , 5 , 7 , ········ }
★ Natural Numbers ★
All such counting numbers are referred as natural numbers. It is denoted by " N ".
Examples :- { 1 , 2 , 3 , 4 , ········ }
★ Whole Numbers ★
All natural numbers including 0 are called whole numbers . It is denoted by " W " .
Examples :- { 0 , 1 , 2 , 3 , ········ }
★ Integers ★
All negative and positive numbers which can be represented on the number line are called integers.
It is denoted by " I " and " z " .
Examples :- { - 2 , - 1 , 0 , 1 , ········ }
★ Rational Numbers ★
The number which is written in the form of where p and q are Integers and q ≠ 0 .
Examples :- { 0 , , , - 4 , ········ }
★ Irrational Numbers ★
The number which cannot be expressed in the form of p/q are called Irrational numbers.
Examples :- { √2 , √3 , √5 , ········ }
Let's understand the concept first .
★ What are twin prime numbers ?
Twin primes are pairs of primes of the type (n, n+2).
Twin primes are two natural numbers the distance between is 2, and which are both prime numbers! {(n,m):n,m∈Prime; m = n+2; m>n }.
Example - { ( 3 ,5 ) , ( 5, 7 ) ······· }
So , Therefore ,
Twin primes between 1 and 50
( 2 , 3 )
( 5 , 7 )
( 11 , 13 )
( 17 , 19 )
( 29 , 31 )
( 41 43)
★ Composite Numbers ★
All the natural numbers except the prime numbers are called composite Numbers.
Examples :- { 4 , 6 , 8 , 10 ········ }
Hence ,
Five composite numbers less than 50.
4
6
8
9
10
Other composite Numbers less than 50 are - 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49.
★ Co - prime numbers ★
Two numbers are coprime if their highest common factor (or greatest common divisor) is 1.
For example - { (2,3), (5,11), (19,23)········ }
Five examples of co-primes
( 2 , 3 )
( 5 , 7 )
( 11 , 13 )
( 17 , 19 )
( 29 , 31 )
( 41 43)
Other Numbers are :-
★ Even Number ★
The number which are divisible by 2 are called even numbers .
Examples :- { 2 , 4 , 6 , 8 , ········ }
★ Odd Numbers ★
The numbers which are not divisble by 2 are called odd numbers .
Examples :- { 3 , 5 , 7 , 9 , ········ }
★ Prime Numbers ★
The number which are divisible by 1 or itself are called prime numbers.
Examples :- { 2 , 3 , 5 , 7 , ········ }
★ Natural Numbers ★
All such counting numbers are referred as natural numbers. It is denoted by " N ".
Examples :- { 1 , 2 , 3 , 4 , ········ }
★ Whole Numbers ★
All natural numbers including 0 are called whole numbers . It is denoted by " W " .
Examples :- { 0 , 1 , 2 , 3 , ········ }
★ Integers ★
All negative and positive numbers which can be represented on the number line are called integers.
It is denoted by " I " and " z " .
Examples :- { - 2 , - 1 , 0 , 1 , ········ }
★ Rational Numbers ★
The number which is written in the form of \frac{p}{q}
q
p
where p and q are Integers and q ≠ 0 .
Examples :- { 0 , \frac{2}{3}
3
2
, \frac{3}{5}
5
3
, - 4 , ········ }
★ Irrational Numbers ★
The number which cannot be expressed in the form of p/q are called Irrational numbers.
Examples :- { √2 , √3 , √5 , ········ }