left-right_truncatable_primes.sf

#!/usr/bin/ruby

# Generate both-truncatable primes of the form "abXcd", such that the following terms are all prime numbers:
#   abXcd
#   abXc
#   bXcd
#   bXc
#   bX
#   Xc

# Definition:
# 1. Removing a digit from either side, the number remains prime.
# 2. Removing both digits, the number is still prime.
# 3. Continuing this process, we end up with X.

# Full sequence for prime numbers X below 10:
#   2, 3, 5, 7, 131, 137, 173, 179, 373, 379, 431, 479, 673, 971, 21319, 33739, 54799, 63793, 66733, 76733, 91373, 91733, 94793, 2913739, 3667333, 9637937, 696379373, 896379373

# See also:
#   https://www.youtube.com/watch?v=azL5ehbw_24
#   https://en.wikipedia.org/wiki/Truncatable_prime

func both_truncatable_primes(p) {

    var seq = [p]

    for n in (1..9) {

        # New left-truncatable prime
        Number("#{n}#{p}").is_prime || next

        for m in ([1, 3, 7, 9]) {

            # New right-truncatable prime
            Number("#{p}#{m}").is_prime || next

            # New left and right truncatable prime
            var t = Number("#{n}#{p}#{m}")

            if (t.is_prime) {
                seq << both_truncatable_primes(t)...
            }
        }
    }

    return seq
}

var seq = []
10.primes.each {|p|
    seq << both_truncatable_primes(p)...
}
say seq.sort