Determines whether integer values are prime numbers.
Value
a logical vector indicating whether each element of n
is a prime number, NA where n exceeds 2^53.
Details
This function is vectorized and returns a logical vector of the same length as the input.
Internally, a fast deterministic primality test for 64-bit integers is used.
Non-integer, negative, missing, or non-finite values result in
FALSE: there the answer is known, it simply is not "prime".
Upper limit
Values above 2^53 (9007199254740992) return NA with
a warning, because for them there is no answer to give. 2^53 is
the largest integer up to which every integer is exactly
representable; above it the representable integers thin out, so the
value that reaches the test need not be the value that was entered: R
parses 9007199254740997, which is prime, as
9007199254740996.
Every representable double above 2^53 is even, so testing the
neighbour would report FALSE for every prime beyond the
bound – silently, and with no way for the caller to notice. For larger
numbers, use gmp::isprime() with a gmp::as.bigz() or
character input.
factorize() carries the same bound but rejects the input
with an error instead. The difference is deliberate: factorize()
answers one number per call element and can refuse the call, whereas a
vectorized predicate should not let a single unrepresentable element
discard the result for all the others.
See also
Other number.theory:
GCD-LCM,
digitSum(),
divisors(),
factorize(),
fibonacci(),
isOdd(),
primes()
Examples
isPrime(2)
#> [1] TRUE
isPrime(1:10)
#> [1] FALSE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
isPrime(c(17, 18, 19))
#> [1] TRUE FALSE TRUE