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# MATHEMATICAL CONCEPTS AND ALGORITHMS – FIBANOCCI, FACTORIAL AND PRIME

## Fibonacci numbers or Fibonacci sequence

The Fibonacci numbers or Fibonacci sequence are the numbers in which every element is the sum of previous two elements.

Example:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

Notes:

• It may start from 0 or 1.
• The Fibonacci sequence is named after Italian mathematician Fibonacci.

Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

For example,

5! = 5 * 4 * 3 * 2 * 1 = 120.

• 0! is 1.
• The notation n! was introduced by Christian Kramp in 1808.

Prime and Composite numbers

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 5 is prime because 1 and 5 are its only positive integer factors. The property of being prime (or not) is called primality.

The first 25 prime numbers (all the prime numbers less than 100) are:

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.

Finding Prime numbers

• A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and sqrt{n}.
• The Sieve of Eratosthenes is another simple algorithm for finding all prime numbers up to a specified integer.

Composite numbers

A natural number greater than 1 that is not a prime number is called a composite number. For example, 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6.

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