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What do you mean by a prime number?
What do you mean by a prime number? What are their special properties?
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3 Replies
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A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In other words, it is a number that cannot be divided evenly by any other number except 1 and itself, without leaving a remainder.
Here are a few examples of prime numbers:
- 2 is the smallest prime number.
- 3, 5, 7, and 11 are prime numbers.
- 13, 17, 19, and 23 are also prime numbers.
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They have two factors, which are 1 and the number itself.
Special properties:
1. The only even prime number is 2.
2. All numbers can be expressed as the product of prime numbers.
3. Writing a number as a product of prime numbers is called a prime factorization of the number.
Example: 34866 = 2 * 3 * 3 * 13 * 149
4. Primes are central in number theory because of the fundamental theorem of arithmetic. The theorem states that ” Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order”.
5 A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.