Use the sieve :)

primeperms.rb

def eratosthenes(n)
  nums = [nil, 1, *2..n]
  (2..Math.sqrt(n)).each do |i|
    (i**2..n).step(i){|m| nums[m] = nil}  if nums[i]
  end
  nums
end

primes_to_million = eratosthenes(1_000_000)

prime_perms = primes_to_million.select { |n|
  n.to_s
   .chars
   .permutation
   .flat_map(&:join)
   .map(&:to_i)
   .all?{ |n| primes_to_million[n] }
}.count

puts prime_perms