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The Brocard conjecture
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The Brocard conjecture asserts that the number of primes, within the interval, between the squares of two subsequent primes is greater than or equal to 4. Although the number of primes within this interval varies to a great degree, there is a common ground, which makes it possible to settle this old conundrum. Three bounds are developed: the least lower bound and the lower/upper bounds. The least lower bound is implemented to prove the conjecture. The lower/upper bounds exploit the shortest such interval, namely between the twin primes. This has been done in order to establish the bounds, on the smallest number of primes within that interval. The research objective was not only to provide a true/false answer, but to clarify some aspects of the distribution of prime numbers within this interval as well.
Title: The Brocard conjecture
Description:
The Brocard conjecture asserts that the number of primes, within the interval, between the squares of two subsequent primes is greater than or equal to 4.
Although the number of primes within this interval varies to a great degree, there is a common ground, which makes it possible to settle this old conundrum.
Three bounds are developed: the least lower bound and the lower/upper bounds.
The least lower bound is implemented to prove the conjecture.
The lower/upper bounds exploit the shortest such interval, namely between the twin primes.
This has been done in order to establish the bounds, on the smallest number of primes within that interval.
The research objective was not only to provide a true/false answer, but to clarify some aspects of the distribution of prime numbers within this interval as well.
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