(Henri Brocard) With the exception of 4 and 9, there are always at least four prime numbers between the square of a prime and the square of the next prime. To put it algebraically, given the th prime (with ), the inequality is always true, where is the prime counting function.
For example, between and there are only two primes: 5 and 7. But between and there are five primes: a prime quadruplet (11, 13, 17, 19) and 23.
This conjecture remains unproven as of 2007. Thanks to computers, brute force searches have shown that the conjecture holds true as high as .
|Date of creation||2013-03-22 16:40:53|
|Last modified on||2013-03-22 16:40:53|
|Last modified by||PrimeFan (13766)|