In mathematics, Bertrand’s Postulate states that there is a prime number in the range 
to 
where n is a natural number and n >= 4. It has been proved by Chebyshev and later by Ramanujan. A lenient form of the postulate states that there exists a prime in range n to 2n for any n(n >= 2).
There exists a prime p for
for all n <= 4. The less stricter form states that there exists a prime p. For
for all n <= 2.
Examples:
For n = 4 and 2*n – 2 = 6,
5 is a prime number in the range (4, 6).
For n = 5 and 2*n – 2 = 8,
7 is a prime number in the range (5, 8).
For n = 6 and 2*n – 2 = 10,
7 is a prime number in the range (6, 10).
For n = 7 and 2*n – 2 = 12,
11 is a prime number in the range (7, 12).
For n = 8 and 2*n – 2 = 14,
11 is a prime number in the range (8, 14).
for all n <= 4. The less stricter form states that there exists a prime p. For 
for all n <= 2. Examples :
Input: n = 4
Output: Prime numbers in range (4, 6) are 5Input: n = 5
Output: Prime numbers in range (5, 8) are 7Input: n = 6
Output: Prime numbers in range (6, 10) are 7
C++
// CPP code to verify Bertrand's postulate// for a given n.#include <bits/stdc++.h>using namespace std;bool isprime(int n){ // check whether a number is prime or not for (int i = 2; i * i <= n; i++) if (n % i == 0) // i is a factor of n return false; return true;}int main(){ int n = 10; // Checking Bertrand's postulate // Presence of prime numbers in range (n, 2n - 2) cout << "Prime numbers in range (" << n << ", " << 2 * n - 2 << ")\n"; for (int i = n + 1; i < 2 * n - 2; i++) if (isprime(i)) cout << i << "\n"; return 0;} |
Java
// Java code to verify Bertrand's // postulate for a given n.import java.io.*;class GFG {static boolean isprime(int n){ // check whether a number // is prime or not for (int i = 2; i * i <= n; i++) if (n % i == 0) // i is a factor of n return false; return true;} // Driver Code public static void main (String[] args) { int n = 10; // Checking Bertrand's postulate // Presence of prime numbers in // range (n, 2n - 2) System.out.println("Prime numbers in range (" + n + ", "+ (2 * n - 2) + ")"); for (int i = n + 1; i < 2 * n - 2; i++) if (isprime(i)) System.out.println(i); }}// This code is contributed // by shiv_bhakt |
Python3
# PHP code to verify # Bertrand's postulate # for a given n.def isprime(n): # check whether a number # is prime or not i = 2; while(i * i <= n): if (n % i == 0): # i is a factor of n return False; i = i + 1; return True;# Driver Coden = 10;# Checking Bertrand's # postulate Presence # of prime numbers in# range (n, 2n - 2)print("Prime numbers in range (" , n , ", ", 2 * n - 2 , ")");i = n + 1;while(i < (2 * n - 2)): if (isprime(i)): print(i); i = i + 1;# This code is contributed by mits |
C#
// C# code to verify Bertrand's // postulate for a given n.using System;class GFG{static bool isprime(int n){ // check whether a number // is prime or not for (int i = 2; i * i <= n; i++) if (n % i == 0) // i is a factor of n return false; return true;}// Driver Codepublic static void Main () { int n = 10; // Checking Bertrand's postulate // Presence of prime numbers in // range (n, 2n - 2) Console.WriteLine("Prime numbers in range (" + n + ", "+ (2 * n - 2) + ")"); for (int i = n + 1; i < 2 * n - 2; i++) if (isprime(i)) Console.WriteLine(i);}}// This code is contributed // by shiv_bhakt |
PHP
<?php// PHP code to verify Bertrand's// postulate for a given n.function isprime($n){ // check whether a number // is prime or not for ($i = 2; $i * $i <= $n; $i++) if ($n % $i == 0) // i is a factor of n return false; return true;}// Driver Code$n = 10;// Checking Bertrand's postulate// Presence of prime numbers in// range (n, 2n - 2)echo "Prime numbers in range (" , $n , ", ", 2 * $n - 2 , ")\n";for ($i = $n + 1; $i < 2 * $n - 2; $i++) if (isprime($i)) echo $i , "\n";// This code is contributed by ajit?> |
Javascript
<script> // Javascript code to verify Bertrand's // postulate for a given n. function isprime(n) { // check whether a number // is prime or not for (let i = 2; i * i <= n; i++) if (n % i == 0) // i is a factor of n return false; return true; } let n = 10; // Checking Bertrand's postulate // Presence of prime numbers in // range (n, 2n - 2) document.write( "Prime numbers in range (" + n + ", "+ (2 * n - 2) + ")" + "</br>" ); for (let i = n + 1; i < 2 * n - 2; i++) if (isprime(i)) document.write(i + "</br>"); </script> |
Prime numbers in range (10, 18) 11 13 17
Time Complexity: O(n*sqrt(n))
Auxiliary Space: O(1)
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