# What is a Prime Number

The question of what prime numbers are, takes us deep into mathematics territory. In this article, we explain what's special about these numbers.

Omkar Phatak

What are They?

A prime number is any natural number that is fully divisible only by itself and the number 1. In other words, it's a number which cannot be factorized into other numbers. For example, 2 is only divisible by 2 itself and 1. 2 can only be factorized into 2 and 1 (i.e. 2 = 2 x 1). So two is in fact the smallest one of them.

Prime Number Theorem

Known as the '

*Fundamental Theorem of Arithmetic*', it states that any number (which is greater than 1), can be factorized into a product of prime numbers and this product is unique. So every composite number, is a unique product of these numbers and their powers. For example, 15 = 1 x 3 x 5, which is a unique product. Remember this theorem as it is one of the most important theorems in all of arithmetic.Chart

So how many prime numbers are there? Mathematicians have pondered about this question for years and proved that they are indeed infinite. Here is a chart showing all those which are lesser than 1000.

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 | 101 | 103 | 107 | 109 | 113 |

127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 |

179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 |

233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 |

283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 |

353 | 359 | 367 | 373 | 379 | 383 | 389 | 397 | 401 | 409 |

419 | 421 | 431 | 433 | 439 | 443 | 449 | 457 | 461 | 463 |

467 | 479 | 487 | 491 | 499 | 503 | 509 | 521 | 523 | 541 |

547 | 557 | 563 | 569 | 571 | 577 | 587 | 593 | 599 | 601 |

607 | 613 | 617 | 619 | 631 | 641 | 643 | 647 | 653 | 659 |

661 | 673 | 677 | 683 | 691 | 701 | 709 | 719 | 727 | 733 |

739 | 743 | 751 | 757 | 761 | 769 | 773 | 787 | 797 | 809 |

811 | 821 | 823 | 827 | 829 | 839 | 853 | 857 | 859 | 863 |

877 | 881 | 883 | 887 | 907 | 911 | 919 | 920 | 937 | 941 |

947 | 953 | 967 | 971 | 977 | 983 | 991 | 997 |

Prime numbers can be looked at as building blocks of composite numbers. There are many interesting theorems and properties related to them, that you should know about.