prime_count: Prime-counting Functions and Estimating the Value of the n-th...
In Ironholds/primes: Fast Functions for Prime Numbers
prime_count R Documentation
Prime-counting Functions and Estimating the Value of the n-th Prime
Description
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.
Usage
prime_count(n, upper_bound)
nth_prime_estimate(n, upper_bound)
Arguments
n
an integer. See Details for more information.
upper_bound
a logical indicating whether to estimate the lower- or
upper bound.
Details
The prime_count function estimates the number of primes \le n.
When upper_bound = FALSE, it is guaranteed to under-estimate for all
n \ge 17.
When upper_bound = TRUE, it holds for all positive n.
The nth_prime_estimate function brackets upper and lower bound values of
the nth prime. It is valid for n \ge 6.
The methods of estimation used here are a few of many alternatives. For
further information, the reader is directed to the References section.
Author(s)
Paul Egeler, MS
References
"Prime-counting function" (2020) Wikipedia. https://en.wikipedia.org/wiki/Prime-counting_function#Inequalities (Accessed 26 Jul 2020).
Ironholds/primes documentation built on Feb. 1, 2024, 1:26 a.m.
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| prime_count | R Documentation |
Prime-counting Functions and Estimating the Value of the n-th Prime
Description
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.
Usage
prime_count(n, upper_bound)
nth_prime_estimate(n, upper_bound)
Arguments
n |
an integer. See Details for more information. |
upper_bound |
a logical indicating whether to estimate the lower- or upper bound. |
Details
The prime_count function estimates the number of primes \le n.
When upper_bound = FALSE, it is guaranteed to under-estimate for all
n \ge 17.
When upper_bound = TRUE, it holds for all positive n.
The nth_prime_estimate function brackets upper and lower bound values of
the nth prime. It is valid for n \ge 6.
The methods of estimation used here are a few of many alternatives. For further information, the reader is directed to the References section.
Author(s)
Paul Egeler, MS
References
"Prime-counting function" (2020) Wikipedia. https://en.wikipedia.org/wiki/Prime-counting_function#Inequalities (Accessed 26 Jul 2020).
R Package Documentation
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