Distribution of Primes

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Euclid proved that the number of prime numbers is infinite. Prime numbers seem to be arranged in an unpredictable way, but sometimes patterns emerge. This Demonstration provides information about the distribution of primes up to the first 5000 positive integers .

[more]

The array on the left consists of cells that each represent a positive integer from 1 to , counting left-to-right, top-to-bottom. Black cells represent prime numbers. The array illustrates the distribution of prime numbers among the positive integers.

The graph on the right shows the cumulative distribution of the primes and its approximation by the formula , which was first conjectured by Gauss and plays a role in the prime number theorem.

[less]

Contributed by: Hector Zenil (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send