This code reuses the function that strips all digits for a number, presented in Euler Problem 30. The solution for this problem also use the is.prime function to test whether a number is a prime, developed for Euler Problem 7.
The following auxiliary functions help to solve the problem:
esieve: Generate primesis_prime: Checks whether a number is primerotate_left: Rotates the a number
# Sieve of Eratosthenes
esieve <- function(x) {
if (x == 1) return(NULL)
if (x == 2) return(n)
l <- 2:x
i <- 1
p <- 2
while (p^2 <= x) {
l <- l[l == p | l %% p!= 0]
i <- i + 1
p <- l[i]
}
return(l)
}
## Check if a number is prime
is_prime <- function(x) {
if (x <= 1) return(FALSE)
if (x == 2 | x == 3) return(TRUE)
primes <- esieve(ceiling(sqrt(x)))
return(all(x %% primes != 0))
}
## Rotate a number to the left
rotate_left <- function(x) {
if (x <= 9) return(x)
i <- 1
y <- vector()
while(x >= 1) {
d <- x %% 10
y[i] <- d
i <- i + 1
x = x %/% 10
}
as.numeric(paste(y[c((length(y) - 1):1, length(y))], collapse = ""))
}
## Check circularity
is_circular_prime <- function(x) {
n <- trunc(log10(x)) + 1
p <- vector(length = n)
for (r in 1:n) {
p[r] <- is_prime(x)
x <- rotate_left(x)
}
all(p)
}
primes <- esieve(1E6)
length(which(sapply(primes, is_circular_prime)))
The main program runs through each of the 78,498 primes below one million, saves their digits in a vector and then cycles the numbers to test for primality of each rotation.