Added to Favorites

Popular Searches

Definitions

Nearby Words

In number theory, Brocard's conjecture is a conjecture that there are at least four prime numbers between (p_{n})^{2} and (p_{n+1})^{2}, for n > 1, where p_{n} is the n^{th} prime number. It is widely believed that this conjecture is true. However, it remains unproven as of 2007.## See also

## References

The number of primes between prime squares is 2, 5, 6, 15, 9, 22, 11, 27, ... .

Legendre's conjecture that there is a prime between consecutive integer squares directly implies that there are at least two primes between prime squares for p_{n} ≥ 3 since p_{n+1} - p_{n} ≥ 2.

Wikipedia, the free encyclopedia © 2001-2006 Wikipedia contributors (Disclaimer)

This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday September 10, 2008 at 13:09:43 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday September 10, 2008 at 13:09:43 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

Copyright © 2015 Dictionary.com, LLC. All rights reserved.