# Prime Numbers

A prime number is a number that is greater than 1 and that is not a product of two smaller numbers. A number greater than 1 that is not a prime number is called a composite number.

For an example `5`

is a prime number because the only way of writing it with
integer factorization we get: `1 x 5`

or `5 x 1`

, which involves only `5`

itself. On the contrary `4`

is not a prime number because we can factor it as:
`1 x 4`

, `2 x 2`

, and `4 x 1`

.

Finding prime numbers manually is not only tedious, but can also be considered impossible once we get to larger numbers such as the current largest known prime number which has 24,862,048 digits. Being that numbers are infinite the list of prime numbers is also infinite, as demonstrated by Euclid in 300 BC. For this reason there are many formulas for finding prime numbers such as prime factorization.

Because I often have to reference this here are the first 100 prime numbers:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|

1-10 | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 |

11-20 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 |

21-30 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 |

31-40 | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 |

41-50 | 179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 |

51-60 | 233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 |

61-70 | 283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 |

71-80 | 353 | 359 | 367 | 373 | 379 | 383 | 389 | 397 | 401 | 409 |

81-90 | 419 | 421 | 431 | 433 | 439 | 443 | 449 | 457 | 461 | 463 |

91-100 | 467 | 479 | 487 | 491 | 499 | 503 | 509 | 521 | 523 | 541 |