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# Prime numbers and composite numbers

## Prime numbers

The numbers which cannot be factored in are called prime numbers. Prime numbers have two factors only, one and the number itself. This means that prime numbers are divisible only by one and the number itself.

Primality is the property of being prime. One can check the primality of a number by trial division test. Start with the smallest number and then increase the number to do the trial division test. One can also find the divisibility of a number by simple rules of divisibility. Prime numbers have wide applicability in various fields of science and technology. Prime numbers are used in abstract algebra, Eisenstein’s criterion, computing for checksums, hash tables, pseudorandom number generators, knot theory, quantum mechanics, evolutionary biology, arts, and literature.

Consider an example, 34866. Its factors are 2 x 3 x 3 x 13 x 149. All these numbers are prime numbers. Hence, these are called prime factors.

## List of prime numbers from 1 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

## Composite numbers

The numbers having more than two factors are called composite numbers. Composite numbers must have factors other than one and the number itself. They are also known as non-prime numbers.

## Types of composite numbers

1. Odd composite numbers: - Every odd integer that is not a prime number is an odd composite number. E.g. 9, 15, 21, 27, 33, etc.
2. Even composite numbers: - Every even integer that is not a prime number is an even composite number. E.g. 4, 6, 8, 10, 12, 14, etc.

## List of composite numbers from 1 to 100

 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30 32 33 34 35 36 38 39 40 42 44 45 46 49 50 51 52 54 55 56 57 58 60 62 63 64 65 66 68 69 70 72 74 75 76 77 78 80 81 82 85 86 87 88 89 90 91 92 93 94 95 96 98 99 100

## Fundamental theorem of arithmetic

It states that every number greater than 1 can be written as a product of two or more prime numbers.

## Fun facts

1. Euclid, a Greek mathematician, examined prime numbers in 300 BC.
2. 2 is the only even prime number. Every other number is divisible by 2. Hence, no other number is an even prime number.
3. 0 and 1 are not prime numbers nor composite numbers.
4. Only 5 is the number that ends with 5 and is a prime number. Every other number that ends with 5 is divisible by 5. Hence, not a prime number.
5. Prime numbers are used in security technology and cryptography.
6. The most significant prime number has 13 million digits, found to date.
7. The most exciting prime number sequence is 6089, 60899, 608999, 6089999, 60899999, 608999999.
8. Many people are confused about whether 11 is a prime number or not. What do you think? Read the property of prime numbers (i.e., they are divisible by 1 and the number itself). Find it out
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