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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. This prime numbers have certain properties. In this page we also explain different types of primes numbers, let us look into it.

Example of prime number:

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

  • 1 is not prime number, since it has only one divisor, namely 1.
  • However, 2 and 3 are prime number, 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.

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Properties of Prime Numbers

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Below are the properties of prime numbers:

  • Numbers of prime numbers are uncountable. i.e., the number of primes is infinite.
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

  • 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 largest known prime is 243,112,609 - 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

  • If p is a prime, is 2p - 1 always square free.
  • 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.

Example: 3, 5, 7, ..............

  • All prime numbers above q are of form q = n + m,

Where 0 < m < q,

And m has no prime factor q.

  • If p is a prime number and a, b are the integers .

If p divides ab ,

Then p divides a or p divides b.

Types of Prime Numbers

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  • Twin prime numbers

Example: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43)

  • Cousin prime numbers

Examples: (3, 7), (7, 11), (13, 17), (19, 23), (37, 41)

  • Balanced prime numbers
Examples: 5, 53, 157, 173, 211, 257, 263

  • Palindromic prime numbers
Example: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919

  • Reversible prime numbers
Example: 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157

  • Pythagorean prime numbers
Example: 5, 13, 17, 29, 37, 41, 53, 61, 73

  • Permutable prime numbers
Example: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79

  • Mersenne prime numbers

Example: 3, 7 , 31, 127, 511, 2047

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