prime_count | R Documentation |
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.
prime_count(n, upper_bound)
nth_prime_estimate(n, upper_bound)
n |
an integer. See Details for more information. |
upper_bound |
a logical indicating whether to estimate the lower- or upper bound. |
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.
Paul Egeler, MS
"Prime-counting function" (2020) Wikipedia. https://en.wikipedia.org/wiki/Prime-counting_function#Inequalities (Accessed 26 Jul 2020).
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