A045336 Palindromic terms from A019546.

2, 3, 5, 7, 353, 373, 727, 757, 32323, 33533, 35353, 35753, 37273, 37573, 72227, 72727, 73237, 75557, 77377, 3222223, 3223223, 3233323, 3252523, 3272723, 3337333, 3353533, 3553553, 3722273, 3732373, 3773773, 7257527, 7327237, 7352537, 7527257, 7722277

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• base

Comments

a(33) = 7352537 is the smallest palindromic prime using all prime digits (see Prime Curios! link). - Bernard Schott, Nov 10 2020

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..12725 (all terms with <= 17 digits; terms 1..330 from Harvey P. Dale)
• Chris K. Caldwell and G. L. Honaker, Jr., 7352537, Prime Curios!

Crossrefs

Cf. A019546 and A002385.

Programs

Mathematica

Select[ Range[ 1, 10^7 ], PrimeQ[ # ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 0 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 1 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 4 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 6 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 8 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 9 ] && RealDigits[ # ][ [ 1 ] ] == Reverse[ RealDigits[ # ][ [ 1 ] ] ] & ]
Table[FromDigits/@Select[Tuples[{2,3,5,7},n],#==Reverse[#]&&PrimeQ[ FromDigits[ #]]&],{n,12}]//Flatten (* Harvey P. Dale, Jun 19 2016 *)
Select[Flatten[Table[FromDigits/@Tuples[{2,3,5,7},n],{n,10}]],PrimeQ[#]&&PalindromeQ[#]&] (* Harvey P. Dale, Mar 24 2025 *)
f@n_ := Prime@n;
g@l_ := FromDigits@# & /@ Table[Join[l, {f@i}, Reverse@l], {i, 4}];
Flatten[g@# & /@ (f@# & /@
     Select[Table[IntegerDigits[n, 5], {n, 2000}], FreeQ[#, 0] &])] //
Select[PrimeQ] (* Hans Rudolf Widmer, Dec 18 2021 *)

Python

from sympy import isprime
from itertools import count, product, takewhile
def primedigpals():
    for d in count(1, 2):
        for p in product("2357", repeat=d//2):
            left = "".join(p)
            for mid in "2357":
                yield int(left + mid + left[::-1])
def aupto(N):
    return list(takewhile(lambda x: x<=N, filter(isprime, primedigpals())))
print(aupto(10**7)) # Michael S. Branicky, Dec 18 2021