Generate Prime Numbers up to Given Limits

Computes all prime numbers less than or equal to each value in n.

Usage

primes(n)

Arguments

n

a numeric vector of positive whole numbers, none exceeding 100,000,000.

Value

an integer vector containing the prime numbers less than or equal to n in ascending order if n is a single number, otherwise a named list of such vectors.

Details

The function is vectorized over n. For a single value, the primes are returned as an integer vector; for several values, a named list is returned, with names corresponding to the input values.

Upper limit

n may not exceed 100,000,000. The limit is a practical one, not a limit of the type: the sieve of Eratosthenes needs one bit per candidate and one integer per prime found, which at 100 million comes to roughly 12.5 MB for the sieve, 23 MB for the 5,761,455 primes, and a peak below about 70 MB once the copy into R is counted. At .Machine$integer.max the same three figures are 268 MB, 105,097,565 primes for 420 MB, and a peak beyond a gigabyte - which is why the integer limit is not a sensible bound here. A substantially larger range would call for a segmented sieve rather than for a larger allocation.

See also

Other number.theory: GCD-LCM, digitSum(), divisors(), factorize(), fibonacci(), isOdd(), isPrime()

Examples

primes(10)
#> [1] 2 3 5 7
primes(c(5, 10))
#> $`5`
#> [1] 2 3 5
#> 
#> $`10`
#> [1] 2 3 5 7
#> 

# the number of primes below a limit
length(primes(1e6))
#> [1] 78498