prime_count

nth_prime_estimate

an integer. See Details for more information.

a logical indicating whether to estimate the lower- or
upper bound.

upper_bound

Functions for estimating \(\pi(n)\)---the number of primes less than
or equal to \(n\)---and for estimating the value of \(p_n\), the n-th
prime number.

Fast functions for dealing with prime numbers, such as testing
whether a number is prime and generating a sequence prime numbers.
Additional functions include finding prime factors and Ruth-Aaron pairs,
finding next and previous prime numbers in the series, finding or estimating
the nth prime, estimating the number of primes less than or equal to an
arbitrary number, computing primorials, prime k-tuples (e.g., twin primes),
finding the greatest common divisor and smallest (least) common multiple,
testing whether two numbers are coprime, and computing Euler's totient
function. Most functions are vectorized for speed and convenience.

Oliver Keyes

primes

Fast Functions for Prime Numbers

Os Keyes

Paul Egeler

prime_count function

<dl><dt>n</dt>
<dd>an integer. See Details for more information.</dd>
<dt>upper_bound</dt>
<dd>a logical indicating whether to estimate the lower- or
upper bound.</dd></dl>

Arguments

Author

Prime-counting Functions and Estimating the Value of the n-th Prime — prime_count

<dl>

<dt>n</dt>
<dd>an integer. See Details for more information.</dd>


<dt>upper_bound</dt>
<dd>a logical indicating whether to estimate the lower- or
upper bound.</dd>

</dl>

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prime_count: Prime-counting Functions and Estimating the Value of the n-th Prime

Description

Usage

Arguments

Author

Details

References