This Python program will help you to verify Legendre\’s Conjecture.
According to Wikipedia “conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. Conjectures such as the Riemann hypothesis or Fermat’s Last Theorem have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.”
Python Program to verify Legendre\’s Conjecture
import math def isprime( n ): i = 2 for i in range (2, int((math.sqrt(n)+1))): if n%i == 0: return False return True def LC( n ): print ( "Primes in the range ", n*n , " and ", (n+1)*(n+1) , " are:" ) for i in range (n*n, (((n+1)*(n+1))+1)): if(isprime(i)): print (i) n = 50 LC(n)