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.
there is always one prime p in the range to where n is any natural number.
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 .
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
Primes in the range 2500 and 2601 are: 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593
Please refer complete article on Legendre’s Conjecture for more details!
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