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Learn About Prime Numbers

What are Prime Numbers?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number is a number that cannot be formed by multiplying two smaller natural numbers.

Properties of Prime Numbers

  1. Uniqueness: Each prime number is unique and cannot be divided by any other numbers except for 1 and itself.
  2. Infinitude: There are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid around 300 BCE.
  3. Prime Factorization: Every integer greater than 1 is either a prime number or can be factored into prime numbers, which are unique to that number (Fundamental Theorem of Arithmetic).

Examples of Prime Numbers

Here are some examples of prime numbers:

  • 2 (the only even prime number)
  • 3
  • 5
  • 7
  • 11
  • 13
  • 17
  • 19
  • 23
  • 29

How to Determine if a Number is Prime

To determine if a number ( n ) is prime:

  1. Check if ( n ) is less than 2. If so, it's not a prime number.
  2. Check if ( n ) is exactly 2. If so, it is a prime number.
  3. For numbers greater than 2, check divisibility from 2 up to the square root of ( n ). If ( n ) is not divisible by any of these numbers, it is prime.