Python Program for Legendre\’s Conjecture

python tutorials and learn python

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 range to where n is any natural number.

for examples-
2 and 3 are the primes in the range to .

5 and 7 are the primes in the range to .

11 and 13 are the primes in the range to .

17 and 19 are the primes in the range to .

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