k_tuple {primes} | R Documentation |
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
: representsc(0,2)
. -
cousin_primes
: representsc(0,4)
. -
third_cousin_primes
: representsc(0,8)
. -
sexy_primes
: representsc(0,6)
. -
sexy_prime_triplets
: representsc(0,6,12)
. (This relationship is unique in thatis 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