Generate and show all primes with strictly ascending decimal digits.

Aside: Try solving without peeking at existing solutions. I had a weird idea for generating
a prime sieve faster, which needless to say didn't pan out. The solution may be p(r)etty trivial
but generating them quickly is at least mildly interesting.
Tip: filtering all 7,027,260 primes below 123,456,789 probably won't kill you, but there is
at least one significantly better and much faster way, needing a mere 511 odd/prime tests.



See also
 OEIS:A052015 - Primes with distinct digits in ascending order


Related

Primes with digits in nondecreasing order (infinite series allowing duplicate digits, whereas this isn't and doesn't)
Pandigital prime (whereas this is the smallest, with gaps in the used digits being permitted)


put (flat 2, 3, 5, 7, sort +*, gather (1..8).map: &recurse ).batch(10)».fmt("%8d").join: "\n";
 
sub recurse ($str) {
    .take for ($str X~ (3, 7, 9)).grep: { .is-prime && [<] .comb };
    recurse $str × 10 + $_ for $str % 10 ^.. 9;
}
 
printf "%.3f seconds", now - INIT now;