## Facts about Prime Numbers

A number of interesting facts related to prime numbers are listed below.

## How many prime numbers are there?

The table below gives you an indication of how many prime numbers there are in all numbers. For example in the range 0 to 10,000,000 there are 664,579 prime numbers.

Range
0 to ? |
No
of Primes |
%
Prime |

10 |
4 | 40.0% |

100 | 25 | 25.0% |

1,000 | 168 | 16.8% |

10,000 | 1,229 | 12.3% |

100,000 | 9,592 | 9.6% |

1,000,000 | 78,498 | 7.8% |

10,000,000 | 664,579 | 6.6% |

100,000,000 | 5,761,455 | 5.8% |

1,000,000,000 | 50,847,534 | 5.1% |

10,000,000,000 | 455,052,511 | 4.6% |

## Are there are infinite number of primes?

Consider this proof that there are an infinite number of primes:

Assume there is a finite number of primes. We then multiply all these primes together. The resulting number will be a number divisible by every single prime. Now add 1. We now have a number that, when you divide it by any prime, will have a remainder of 1. That means we have just discovered another prime number.

This proof was proposed by Euclid in his work Elements (Book IX, Proposition 20) written by the Greek mathematician Euclid in Alexandria around 300 BC.

## Is 1 Prime?

This is a good question. One is not a prime number. By definition a prime number is a number greater than 1 that has no divisors other than 1 and itself.

One is also not a composite number; a composite number can be defined as "any postive integer greater than 1 that has at least one positive divisor other than 1 and itself.