Trait Primorial

pub trait Primorial {
    // Required methods
    fn primorial(n: u64) -> Self;
    fn product_of_first_n_primes(n: u64) -> Self;
}

Required Methods

fn primorial(n: u64) -> Self

fn product_of_first_n_primes(n: u64) -> Self

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl Primorial for u8

fn primorial(n: u64) -> u8

Computes the primorial of a number: the product of all primes less than or equal to it.

The product_of_first_n_primes function is similar; it computes the primorial of the $n$th prime.

If the input is too large, the function panics. For a function that returns None instead, try checked_primorial.

$$ f(n) = n\# = \prod_{p \leq n \atop p \ \text {prime}} p. $$

$n\# = O(e^{(1+o(1))n})$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

fn product_of_first_n_primes(n: u64) -> u8

Computes the product of the first $n$ primes.

The primorial function is similar; it computes the product of all primes less than or equal to $n$.

If the input is too large, the function panics. For a function that returns None instead, try checked_product_of_first_n_primes.

$$ f(n) = p_n\# = \prod_{k=1}^n p_n, $$ where $p_n$ is the $n$th prime number.

$p_n\# = O\left ( \left ( \frac{1}{e}k\log k\left ( \frac{\log k}{e^2}k \right )^{1/\log k} \right )^k \omega(1)\right )$.

This asymptotic approximation is due to Bart Michels.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Primorial for u16

fn primorial(n: u64) -> u16

Computes the primorial of a number: the product of all primes less than or equal to it.

The product_of_first_n_primes function is similar; it computes the primorial of the $n$th prime.

If the input is too large, the function panics. For a function that returns None instead, try checked_primorial.

$$ f(n) = n\# = \prod_{p \leq n \atop p \ \text {prime}} p. $$

$n\# = O(e^{(1+o(1))n})$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

fn product_of_first_n_primes(n: u64) -> u16

Computes the product of the first $n$ primes.

The primorial function is similar; it computes the product of all primes less than or equal to $n$.

If the input is too large, the function panics. For a function that returns None instead, try checked_product_of_first_n_primes.

$$ f(n) = p_n\# = \prod_{k=1}^n p_n, $$ where $p_n$ is the $n$th prime number.

$p_n\# = O\left ( \left ( \frac{1}{e}k\log k\left ( \frac{\log k}{e^2}k \right )^{1/\log k} \right )^k \omega(1)\right )$.

This asymptotic approximation is due to Bart Michels.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Primorial for u32

fn primorial(n: u64) -> u32

Computes the primorial of a number: the product of all primes less than or equal to it.

The product_of_first_n_primes function is similar; it computes the primorial of the $n$th prime.

If the input is too large, the function panics. For a function that returns None instead, try checked_primorial.

$$ f(n) = n\# = \prod_{p \leq n \atop p \ \text {prime}} p. $$

$n\# = O(e^{(1+o(1))n})$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

fn product_of_first_n_primes(n: u64) -> u32

Computes the product of the first $n$ primes.

The primorial function is similar; it computes the product of all primes less than or equal to $n$.

If the input is too large, the function panics. For a function that returns None instead, try checked_product_of_first_n_primes.

$$ f(n) = p_n\# = \prod_{k=1}^n p_n, $$ where $p_n$ is the $n$th prime number.

$p_n\# = O\left ( \left ( \frac{1}{e}k\log k\left ( \frac{\log k}{e^2}k \right )^{1/\log k} \right )^k \omega(1)\right )$.

This asymptotic approximation is due to Bart Michels.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Primorial for u64

fn primorial(n: u64) -> u64

Computes the primorial of a number: the product of all primes less than or equal to it.

The product_of_first_n_primes function is similar; it computes the primorial of the $n$th prime.

If the input is too large, the function panics. For a function that returns None instead, try checked_primorial.

$$ f(n) = n\# = \prod_{p \leq n \atop p \ \text {prime}} p. $$

$n\# = O(e^{(1+o(1))n})$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

fn product_of_first_n_primes(n: u64) -> u64

Computes the product of the first $n$ primes.

The primorial function is similar; it computes the product of all primes less than or equal to $n$.

If the input is too large, the function panics. For a function that returns None instead, try checked_product_of_first_n_primes.

$$ f(n) = p_n\# = \prod_{k=1}^n p_n, $$ where $p_n$ is the $n$th prime number.

$p_n\# = O\left ( \left ( \frac{1}{e}k\log k\left ( \frac{\log k}{e^2}k \right )^{1/\log k} \right )^k \omega(1)\right )$.

This asymptotic approximation is due to Bart Michels.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Primorial for u128

fn primorial(n: u64) -> u128

Computes the primorial of a number: the product of all primes less than or equal to it.

The product_of_first_n_primes function is similar; it computes the primorial of the $n$th prime.

If the input is too large, the function panics. For a function that returns None instead, try checked_primorial.

$$ f(n) = n\# = \prod_{p \leq n \atop p \ \text {prime}} p. $$

$n\# = O(e^{(1+o(1))n})$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

fn product_of_first_n_primes(n: u64) -> u128

Computes the product of the first $n$ primes.

The primorial function is similar; it computes the product of all primes less than or equal to $n$.

If the input is too large, the function panics. For a function that returns None instead, try checked_product_of_first_n_primes.

$$ f(n) = p_n\# = \prod_{k=1}^n p_n, $$ where $p_n$ is the $n$th prime number.

$p_n\# = O\left ( \left ( \frac{1}{e}k\log k\left ( \frac{\log k}{e^2}k \right )^{1/\log k} \right )^k \omega(1)\right )$.

This asymptotic approximation is due to Bart Michels.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Primorial for usize

fn primorial(n: u64) -> usize

Computes the primorial of a number: the product of all primes less than or equal to it.

The product_of_first_n_primes function is similar; it computes the primorial of the $n$th prime.

If the input is too large, the function panics. For a function that returns None instead, try checked_primorial.

$$ f(n) = n\# = \prod_{p \leq n \atop p \ \text {prime}} p. $$

$n\# = O(e^{(1+o(1))n})$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

fn product_of_first_n_primes(n: u64) -> usize

Computes the product of the first $n$ primes.

The primorial function is similar; it computes the product of all primes less than or equal to $n$.

If the input is too large, the function panics. For a function that returns None instead, try checked_product_of_first_n_primes.

$$ f(n) = p_n\# = \prod_{k=1}^n p_n, $$ where $p_n$ is the $n$th prime number.

$p_n\# = O\left ( \left ( \frac{1}{e}k\log k\left ( \frac{\log k}{e^2}k \right )^{1/\log k} \right )^k \omega(1)\right )$.

This asymptotic approximation is due to Bart Michels.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

Implementors