k_tuple: Prime _k_-tuples

In Ironholds/primes: Fast Functions for Prime Numbers

Prime k-tuples

Description

Use prime k-tuples to create lists of twin primes, cousin primes, prime triplets, and so forth.

Usage

k_tuple(min, max, tuple)

sexy_prime_triplets(min, max)

twin_primes(min, max)

cousin_primes(min, max)

sexy_primes(min, max)

third_cousin_primes(min, max)

Arguments

min	the lower bound of the sequence.
max	the upper bound of the sequence.
tuple	an integer vector representing the target k-tuple pattern.

Details

You can construct your own tuples and generate series of primes using k_tuple; however, there are functions that exist for some of the named relationships. They are listed below.

• twin_primes: represents c(0,2).

• cousin_primes: represents c(0,4).

• third_cousin_primes: represents c(0,8).

• sexy_primes: represents c(0,6).

• sexy_prime_triplets: represents c(0,6,12). (This relationship is unique in that p + 18 is guaranteed to be composite.)

The term "third cousin primes" is of the author's coinage. There is no canonical name for that relationship to the author's knowledge.

Value

A list of vectors of prime numbers satisfying the condition of tuple.

Author(s)

Paul Egeler, MS

Examples

# All twin primes up to 13
twin_primes(2, 13) # Identical to `k_tuple(2, 13, c(0,2))`
## [[1]]
## [1] 3 5
##
## [[2]]
## [1] 5 7
##
## [[3]]
## [1] 11 13

# Some prime triplets
k_tuple(2, 19, c(0,4,6))
## [[1]]
## [1]  7 11 13
##
## [[2]]
## [1] 13 17 19

Ironholds/primes documentation built on Feb. 1, 2024, 1:26 a.m.