This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
120121 is such a number because 120121, 121021 (upside down), 151051 (mirror) and 150151 are all prime. (This is the smallest one in which all four numbers are distinct.)
lst1={2,5};
startQ[n_]:=First[IntegerDigits[n]]==1;
subQ[n_]:=Module[{lst={0,1,2,5,8}},SubsetQ[lst,Union[IntegerDigits[n]]]];
rev[n_]:=Reverse[IntegerDigits[n]];
updown[n_]:=FromDigits[rev[n]];
mirror[n_]:=FromDigits[rev[n]/.{2-> 5,5-> 2}];
updownmirror[n_]:=FromDigits[rev[mirror[n]]];
lst2=Select[Range@188801,And[startQ[#],subQ[#],PrimeQ[#],PrimeQ[updown[#]],PrimeQ[mirror[#]],PrimeQ[updownmirror[#]]]&];
Join[lst1,lst2] (* Ivan N. Ianakiev, Oct 08 2015 *)
from sympy import isprime
from itertools import count, islice, product
def t(s): return s.translate({ord("2"):ord("5"), ord("5"):ord("2")})
def ok(s): # s is a string of digits
return all(isprime(int(w)) for w in [s, s[::-1], t(s), t(s[::-1])])
def agen(): # generator of terms
yield from (2, 5)
for d in count(2):
for mid in product("01258", repeat=d-2):
s = "1" + "".join(mid) + "1"
if ok(s): yield int(s)
print(list(islice(agen(), 35))) # Michael S. Branicky, Apr 27 2024
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