sidef-scripts/Math/generate_primes_with_prime_digits.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 08 August 2021
# https://github.com/trizen

# Generate prime numbers that have only prime digits (in a given base).

# See also:
#   https://oeis.org/A019546
#   https://rosettacode.org/wiki/Extra_primes

func primes_with_prime_digits(upto, base = 10) {

    upto = prev_prime(upto+1)

    var list = []
    var digits = @(^base)

    var prime_digits = digits.grep { .is_prime }
    var end_digits   = prime_digits.grep { .is_coprime(base) }

    list << prime_digits.grep { !.is_coprime(base) }...

    for k in (0 .. upto.ilog(base)) {
        prime_digits.variations_with_repetition(k, {|*a|
            var v = a.digits2num(base)
            end_digits.each {|d|
                var n = (v*base + d)
                list << n if (n.is_prime && (n <= upto))
            }
        })
    }

    list.sort
}

say primes_with_prime_digits(1e4)

__END__
[2, 3, 5, 7, 23, 37, 53, 73, 223, 227, 233, 257, 277, 337, 353, 373, 523, 557, 577, 727, 733, 757, 773, 2237, 2273, 2333, 2357, 2377, 2557, 2753, 2777, 3253, 3257, 3323, 3373, 3527, 3533, 3557, 3727, 3733, 5227, 5233, 5237, 5273, 5323, 5333, 5527, 5557, 5573, 5737, 7237, 7253, 7333, 7523, 7537, 7573, 7577, 7723, 7727, 7753, 7757]