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Properties of Prime Numbers

Natural numbers are either prime or composite numbers. A prime number is a natural number that can only be divided by one and itself. In other words, it has exactly two factors. When we factorize a number we will write it as a multiple of prime numbers.

Examples of prime numbers:

 1. The number 7 can only be divided by 1 and 7, so 7 is a prime number.

      1 is not prime, since it has only one divisor, namely 1.
      However, 2 and 3 are prime, since they have exactly two divisors, namely 1 and 2, and 1 and 3, respectively.

  2 . Prime numbers up to 100:

 2
 3  5 7 11
 13  17  19  23 29
 31  37  41  43 47
 53  59  61  67 71
 73  79  83  89 97
              
Below are the properties of prime numbers
  • Prime numbers are uncountable. Example:  2, 3, 5, 7, .................
  • Every Prime number have exactly two factors or divisors. Example: 13 is the prime  number, the divisor of 13 are 1 and 13.
  • Number of even primes is one. Example:  2, is a even prime number.
  • G.C.D of co-prime numbers is always one. Example: 5 and 7 are the co-primes G.C.D of 5 and 7 is 1.
  • The general formula for generate the primes.
           Formula: N = (2p −1) with p equal to the primes 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107 etc.
  • The Twin Primes Conjecture that there are infinitely many pairs of primes only 2 apart.
  • The term odd prime refers to any prime number greater than 2.
  • All prime numbers above q are of form q $\neq$ n + m,
            where 0 < m < q, and m has no prime factor less than equal to q. 
  • Let p is a prime number and a, b are the integers
                         If p divides ab, then p divides a or p divides b.

Related Calculators
Calculate Prime Number Calculate Prime Factors
Find Prime Factorization Calculator Prime Factorization Tree Calculator
 

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