Show Summary Details

# p. 162. The unending sequence of primes

• Peter M. Higgins

### Abstract

‘The unending sequence of primes’ asks: How can we be sure that primes do not become extinct? A number of mathematical proofs have shown this. It can easily be shown that all primes are within one number of a multiple of six. Euclid outlined the infinity of primes by saying there must be a prime number within a certain range of numbers, built on by Johann Dirichlet who mathematically proved the overall frequency of the primes. Gauss used the natural logarithm to give an overall picture of prime distribution. Unfortunately, there are currently no genuinely useful formulas for determining prime numbers.

Access to the complete content on Very Short Introductions online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.