勒让德猜想的Python程序

它说在任何两个连续的自然数（n = 1, 2, 3, 4, 5, ...）平方之间总是有一个素数。这称为勒让德猜想。
猜想：猜想是基于不完整信息的命题或结论，但尚未找到任何证据，即没有被证明或证伪。

Mathematically,
there is always one prime p in the range $n^2$ to $(n + 1)^2$ where n is any natural number.

for examples-
2 and 3 are the primes in the range $1^2$ to $2^2$.

5 and 7 are the primes in the range $2^2$ to $3^2$.

11 and 13 are the primes in the range $3^2$ to $4^2$.

17 and 19 are the primes in the range $4^2$ to $5^2$.

例子：

Input : 4 
output: Primes in the range 16 and 25 are:
        17
        19
        23

解释：这里 4 ² = 16 和 5 ² = 25
因此，16 到 25 之间的素数是 17、19 和 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 = 50
LegendreConjecture(n)
  
# Contributed by _omg

输出 ：

Primes in the range 2500 and 2601 are:
2503
2521
2531
2539
2543
2549
2551
2557
2579
2591
2593

详情请参阅勒让德猜想的完整文章！