cat2:= (a,b) -> 10*a+b;
cat3:= (a,b,c) -> 100*a+10*b+c:
cat4:= (a,b,c,d) -> 1000*a+100*b+10*c+d:
`r-`:= (a,b) -> b-a:
`r/`:= (a,b) -> b/a:
`r^`:= (a,b) -> b^a:
pdigs:= {2,3,5,7}:
R:= {}:
for p in combinat:-permute(pdigs) do
  a:= p[1]; b:= p[2]; c:= p[3]; d:= p[4];
  v:= cat4(op(p));
  if isprime(v) then R:= R union {v}; fi;
  for e in [`+`,`-`,`*`,`/`,`^`] do
    v:= e(cat3(a,b,c),d);
    if v::integer and isprime(v) then R:= R union {v} fi
  od;
  for e in [`-`,`/`,`^`] do
    v:= e(a,cat3(b,c,d));
    if v::integer and isprime(v) then R:= R union {v} fi
  od;
  for e in [`+`,`-`,`*`,`/`,`^`,cat2] do
    vab:= e(a,b);
    for f in [`+`,`-`,`*`,`/`,`^`,cat2] do
        vcd:= f(c,d);
        for g in [`+`,`-`,`*`,`/`,`^`] do
          if g = `/` and vcd = 0 then next fi;
          if g = `^` and vab = 0 then next fi;
          v:= g(vab,vcd);
          if v::integer and isprime(v) then R:= R union {v} fi;
    od od;
    for f in {`+`,`-`,`*`,`/`,`^`,`r-`,`r/`,`r^`} do
      if (f = `/` and vcd = 0) or (f = `r^` and vcd = 0) then next fi; 
      vcab:= f(c,vab);
      for g in {`+`,`-`,`*`,`/`,`^`,`r-`,`r/`} do
        if (g = `/` and vcab = 0) or (g = `^` and vbcd <> 1) then next fi;  
        v:= g(d,vcab);
        if v::integer and isprime(v) then R:= R union {v} fi
od od od od:
sort(convert(R,list));