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)


   extend=: {{ y;(1+each i._1+{.y),L:0 y }}
   $(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9
100
   10 10$(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9
     2      3     13     23       5       7      17      37       47       67
   127    137    347    157     257     457     167     367      467     1237
  2347   2357   3457   1367    2467    3467    1567    4567    12347    12457
 13457  13567  23567 123457  124567      19      29      59       79       89
   139    239    149    349     359     269     569     179      379      479
   389   1249   1259   1459    2459    3469    1279    1579     2579     4679
  1289   2389   1489   2689    5689    1789    2789    4789    23459    13469
 12569  12379  12479  13679   34679   15679   25679   12589    34589    12689
 23689  13789  23789 123479  124679  235679  145679  345679   234589   345689
134789 125789 235789 245789 1245689 1234789 1235789 1456789 12356789 23456789
   timex'(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9' NB. seconds (take with grain of salt)
0.003818
 