Python Program for Legendre\’s Conjecture
It says that there is always one prime number between any two consecutive natural number\’s(n = 1, 2, 3, 4, 5, …) square. This is called Legendre\’s Conjecture.
Conjecture: A conjecture is a proposition or conclusion based upon incompleate information to which no proof has been found i.e it has not been proved or disproved.
Mathematically,
there is always one prime p in the rangeto
where n is any natural number.
for examples-
2 and 3 are the primes in the rangeto
.
5 and 7 are the primes in the range
.
11 and 13 are the primes in the range
.
17 and 19 are the primes in the range
.
Examples:
Input : 4
output: Primes in the range 16 and 25 are:
17
19
23
Explanation: Here 42 = 16 and 52 = 25
Hence, prime numbers between 16 and 25 are 17, 19 and 23.
Input : 10
Output: Primes in the range 100 and 121 are:
101
103
107
109
113
# Python program to verify Legendre\'s Conjecture # for a given n 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 LegendreConjecture( 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 = 50LegendreConjecture(n) # |
Output :
Primes in the range 2500 and 2601 are: 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593