find which of the following number are prime
Answers
Some interesting fact about Prime numbers
2 , 3 ,5 ,7 ,11 ,13 ,17 , 19 etc
Two is the only even Prime number.
Every prime number can represented in form of 6n+1 or 6n-1 except 2 and 3, where n is natural number.
Two and Three are only two consecutive natural numbers which are prime too.
Goldbach Conjecture: Every even integer greater than 2 can be expressed as the sum of two primes.
Wilson Theorem : Wilson’s theorem states that a natural number p > 1 is a prime number if and only if (p - 1) ! ≡ -1 mod p OR (p - 1) ! ≡ (p-1) mod p
Fermat’s Little Theorem: If n is a prime number, then for every a, 1 <= a < n,an-1 ≡ 1 (mod n) OR an-1 % n = 1
Prime Number Theorem : The probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n.
Lemoine’s Conjecture : Any odd integer greater than 5 can be expressed as a sum of an odd prime (all primes other than 2 are odd) and an even semiprime. A semiprime number is a product of two prime numbers. This is called Lemoine’s conjecture.
How we check whether a number is Prime or not?
Naive solution.
A naive solution is to iterate through all numbers from 2 to n-1 and for every number check if it divides n. If we find any number that divides, we return false.
Answer:
A NUMBER WHICH IS DIVISIBLE BY 1 OR ITSELF
( FOR EXAMPLE ) 2,3,5,7,11,13 etc