Prime Numbers
Prime Number
Any Natural number greater than \(1\), which is divisible by \(1\) and only by itself is called Prime Number.
\(2\), \(3\), \(5\), \(7\), \(11\) etc.
\(2\) is the smallest Prime Number.
Prime number cannot be represented by a rectangle or square.
Composite Number
Any Natural number, which is greater than \(1\) and is not a Prime Number is called a Composite Number.
\(4\), \(6\), \(8\), \(9\), \(10\) etc.
\(1\) is neither a Prime Number nor Composite Number.
Composite number can be represented by a rectangle or square.
Coprimes
Two numbers are called to be coprime or co-prime if they have only \(1\) as common factor.
In other way, we can say if greatest common divisor of two numbers is 1, then the two numbers are coprimes.
\((2,3)\), \((14,15)\), \((8,13)\) etc.
Twin Primes
Two numbers are called Twin Primes if they differ by 2 only or we can say that there is only one composite number between them. One prime number can be 2 more or 2 less than another prime number.
\((3,5)\), \((29,31)\), \((71,73)\) etc.
Prime Triplets
A set of three consecutive Prime Numbers if the smallest and the largest differ by 6 and must be in the form of (p, p + 2, p + 6) is called a Prime Triplet.
\((5,7,11)\)
Why?
Because, 5, 7 and 11 is in the form of p, p + 2, p + 6
where p = 5
p + 2 = 5 + 2 = 7
and p + 6 = 5 + 6 = 11