A007500 -id:A007500 - cp's OEIS frontend

A002385 Palindromic primes: prime numbers whose decimal expansion is a palindrome.

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181, 18481, 19391, 19891, 19991

Offset: 1

N. J. A. Sloane, Simon Plouffe

Every palindrome with an even number of digits is divisible by 11, so 11 is the only member of the sequence with an even number of digits. - David Wasserman, Sep 09 2004
This holds in any number base A006093(n), n>1. - Lekraj Beedassy, Mar 07 2005 and Dec 06 2009
The log-log plot shows the fairly regular structure of these numbers. - T. D. Noe, Jul 09 2013
Conjecture: The only primes with palindromic prime indices that are palindromic primes themselves are 3, 5 and 11. Tested for the primes with the first 8000000 palindromic prime indices. - Ivan N. Ianakiev, Oct 10 2014
It follows from the above conjecture that 2 is the only k such that k, prime(k), prime(m) = k + prime(k) and m are all palindromic primes. - Ivan N. Ianakiev, Mar 17 2025
Banks, Hart, and Sakata derive a nontrivial upper bound for the number of prime palindromes n <= x as x -> oo. It follows that almost all palindromes are composite. The results hold in any base. The authors use Weil's bound for Kloosterman sums. - Jonathan Sondow, Jan 02 2018
Number of terms < 100^k, k >= 1: 5, 20, 113, 781, 5953, 47995, 401698, .... - Robert G. Wilson v, Jan 03 2018, corrected by M. F. Hasler, Dec 19 2024
Initially the above comment listed 4, 20, 113, ... which is the number of terms less than 10, 1000, 10^5, ..., i.e., up to 10^(2k-1), k >= 1. The number of terms < 10^k are the cumulative sums of A016115(n) (number of prime palindromes with n digits) up to n = k. - M. F. Hasler, Dec 19 2024

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 228.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 120-121.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, Table of n, a(n) for n = 1..47995 (all palindromic primes with fewer than 12 digits), Oct 14 2015, extending earlier b-files from T. D. Noe and A. Olah.
W. D. Banks, D. N. Hart, and M. Sakata, Almost all palindromes are composite, Math. Res. Lett., 11 No. 5-6 (2004), 853-868.
K. S. Brown, On General Palindromic Numbers
C. K. Caldwell, "Top Twenty" page, Palindrome
Patrick De Geest, World!Of Palindromic Primes
Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv:2008.06864 [math.CO], 2020. Mentions this sequence.
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Dmytro S. Inosov and Emil Vlasák, Cryptarithmically unique terms in integer sequences, arXiv:2410.21427 [math.NT], 2024. See pp. 10, 18.
T. D. Noe, Log-log plot of the first 401696 terms
I. Peterson, Math Trek, Palindromic Primes
Phakhinkon Phunphayap and Prapanpong Pongsriiam, Reciprocal sum of palindromes, arXiv:1803.00161 [math.CA], 2018.
M. Shafer, First 401066 Palprimes
Eric Weisstein's World of Mathematics, Palindromic Number
Eric Weisstein's World of Mathematics, Palindromic Prime
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Wikipedia, Palindromic prime
Index entries for sequences related to palindromes

A007500 = this sequence union A006567.
Subsequence of A188650; A188649(a(n)) = a(n); see A033620 for multiplicative closure. [Reinhard Zumkeller, Apr 11 2011]
Cf. A016041, A029732, A069469, A117697, A046942, A032350 (Palindromic nonprime numbers).
Cf. A016115 (number of prime palindromes with n digits).

Filtered([1..20000],n->IsPrime(n) and ListOfDigits(n)=Reversed(ListOfDigits(n))); # Muniru A Asiru, Mar 08 2019

a002385 n = a002385_list !! (n-1)
a002385_list = filter ((== 1) . a136522) a000040_list
-- Reinhard Zumkeller, Apr 11 2011

ff := proc(n) local i,j,k,s,aa,nn,bb,flag; s := n; aa := convert(s,string); nn := length(aa); bb := ``; for i from nn by -1 to 1 do bb := cat(bb,substring(aa,i..i)); od; flag := 0; for j from 1 to nn do if substring(aa,j..j)<>substring(bb,j..j) then flag := 1 fi; od; RETURN(flag); end; gg := proc(i) if ff(ithprime(i)) = 0 then RETURN(ithprime(i)) fi end;
rev:=proc(n) local nn, nnn: nn:=convert(n,base,10): add(nn[nops(nn)+1-j]*10^(j-1),j=1..nops(nn)) end: a:=proc(n) if n=rev(n) and isprime(n)=true then n else fi end: seq(a(n),n=1..20000); # rev is a Maple program to revert a number - Emeric Deutsch, Mar 25 2007
# A002385 Gets all base-10 palindromic primes with exactly d digits, in the list "Res"
d:=7; # (say)
if d=1 then Res:= [2,3,5,7]:
elif d=2 then Res:= [11]:
elif d::even then
    Res:=[]:
else
    m:= (d-1)/2:
    Res2 := [seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1)]:
    Res:=[]: for x in Res2 do if isprime(x) then Res:=[op(Res),x]; fi: od:
fi:
Res; # N. J. A. Sloane, Oct 18 2015

Select[ Prime[ Range[2100] ], IntegerDigits[#] == Reverse[ IntegerDigits[#] ] & ]
lst = {}; e = 3; Do[p = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[p], AppendTo[lst, p]], {n, 10^e - 1}]; Insert[lst, 11, 5] (* Arkadiusz Wesolowski, May 04 2012 *)
Join[{2,3,5,7,11},Flatten[Table[Select[Prime[Range[PrimePi[ 10^(2n)]+1, PrimePi[ 10^(2n+1)]]],# == IntegerReverse[#]&],{n,3}]]] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Apr 22 2016 *)
genPal[n_Integer, base_Integer: 10] := Block[{id = IntegerDigits[n, base], insert = Join[{{}}, {# - 1} & /@ Range[base]]}, FromDigits[#, base] & /@ (Join[id, #, Reverse@id] & /@ insert)]; k = 1; lst = {2, 3, 5, 7}; While[k < 19, p = Select[genPal[k], PrimeQ];
If[p != {}, AppendTo[lst, p]]; k++]; Flatten@ lst (* RGWv *)
Select[ Prime[ Range[2100]], PalindromeQ] (* Jean-François Alcover, Feb 17 2018 *)
NestList[NestWhile[NextPrime, #, ! PalindromeQ[#2] &, 2] &, 2, 41] (* Jan Mangaldan, Jul 01 2020 *)

is(n)=n==eval(concat(Vecrev(Str(n))))&&isprime(n) \\ Charles R Greathouse IV, Nov 20 2012

forprime(p=2,10^5, my(d=digits(p,10)); if(d==Vecrev(d),print1(p,", "))); \\ Joerg Arndt, Aug 17 2014

A002385_row(n)=select(is_A002113, primes([10^(n-1),10^n])) \\ Terms with n digits. For larger n, better filter primes in palindromes. - M. F. Hasler, Dec 19 2024

from itertools import chain
from sympy import isprime
A002385 = sorted((n for n in chain((int(str(x)+str(x)[::-1]) for x in range(1,10**5)),(int(str(x)+str(x)[-2::-1]) for x in range(1,10**5))) if isprime(n))) # Chai Wah Wu, Aug 16 2014

from sympy import isprime
A002385 = [*filter(isprime, (int(str(x) + str(x)[-2::-1]) for x in range(10**5)))]
A002385.insert(4, 11)  # Yunhan Shi, Mar 03 2023

from sympy import isprime
from itertools import count, islice, product
def A002385gen(): # generator of palprimes
    yield from [2, 3, 5, 7, 11]
    for d in count(3, 2):
        for last in "1379":
            for p in product("0123456789", repeat=d//2-1):
                left = "".join(p)
                for mid in [[""], "0123456789"][d&1]:
                    t = int(last + left + mid + left[::-1] + last)
                    if isprime(t):
                        yield t
print(list(islice(A002385gen(), 46))) # Michael S. Branicky, Apr 13 2025

[n for n in (2..18181) if is_prime(n) and Word(n.digits()).is_palindrome()] # Peter Luschny, Sep 13 2018

Intersection of A000040 (primes) and A002113 (palindromes).
A010051(a(n)) * A136522(a(n)) = 1. [Reinhard Zumkeller, Apr 11 2011]
Complement of A032350 in A002113. - Jonathan Sondow, Jan 02 2018

More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000

Comment from A006093 moved here by Franklin T. Adams-Watters, Dec 03 2009

A006567 Emirps (primes whose reversal is a different prime).

Original entry on oeis.org

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193, 1201

Offset: 1

N. J. A. Sloane

A palindrome is a word that when written in reverse results in the same word. for example, "racecar" reversed is still "racecar". Related to palindromes are semordnilaps. These are words that when written in reverse result in a distinct valid word. For example, "stressed" written in reverse is "desserts". Not all words are palindromes or semordnilaps. While certainly not all numbers are palindromes, all non-palindromic numbers when written in reverse will form semordnilaps. Narrowing to primes brings back the same trichotomy as with words: some numbers are emirps, some numbers are palindromic primes, but some words are neither.

The term "emirp" was coined by the American mathematician Jeremiah Farrell (1937-2022). - Amiram Eldar, Jun 11 2021

Martin Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 230.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 1..10000
Chris K. Caldwell, The Prime Glossary, emirp.
Brady Haran and N. J. A. Sloane, What Number Comes Next?, Numberphile video, 2018.
Eric Weisstein's World of Mathematics, Emirp.
Wikipedia, Emirp.

Cf. A003684, A007628 (subsequence), A046732, A048051, A048052, A048053, A048054, A048895, A004086 (read n backwards).

A007500 is the union of A002385 and this sequence.

a006567 n = a006567_list !! (n-1)
a006567_list = filter f a000040_list where
   f p = a010051' q == 1 && q /= p  where q = a004086 p
-- Reinhard Zumkeller, Jul 16 2014

[ n : n in [1..1194] | n ne rev and IsPrime(n) and IsPrime(rev) where rev is Seqint(Reverse(Intseq(n))) ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

read("transforms") ; isA006567 := proc(n) local R ; if isprime(n) then R := digrev(n) ; isprime(R) and R <> n ; else false; end if; end proc:
A006567 := proc(n) option remember ; local a; if n = 1 then 13; else a := nextprime(procname(n-1)) ; while not isA006567(a) do a := nextprime(a) ; end do; return a; end if; end proc:
seq(A006567(n),n=1..120) ; # R. J. Mathar, May 24 2010

fQ[n_] := Block[{idn = IntegerReverse@ n}, PrimeQ@ idn && n != idn]; Select[Prime@ Range@ 200, fQ] (* Santi Spadaro, Oct 14 2001 and modified by Robert G. Wilson v, Nov 08 2015 *)
Select[Prime[Range[5,200]],PrimeQ[IntegerReverse[#]]&&!PalindromeQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 11 2021 *)

is(n)=my(r=eval(concat(Vecrev(Str(n)))));isprime(r)&&r!=n&&isprime(n) \\ Charles R Greathouse IV, Nov 20 2012

select( {is_A006567(n,r=fromdigits(Vecrev(digits(n))))=isprime(r)&&r!=n&&isprime(n)}, primes(200)) \\ M. F. Hasler, Jan 31 2020

from sympy import prime, isprime
A006567 = [p for p in (prime(n) for n in range(1,10**6)) if str(p) != str(p)[::-1] and isprime(int(str(p)[::-1]))] # Chai Wah Wu, Aug 14 2014

from sympy import isprime, nextprime
def emirps(start=1, end=float('inf')): # generator for emirps in start..end
    p = nextprime(start-1)
    while p <= end:
        s = str(p)
        if s[0] in "24568":
            p = nextprime((int(s[0])+1)*10**(len(s)-1)); continue
        revp = int(s[::-1])
        if p != revp and isprime(revp): yield p
        p = nextprime(p)
print(list(emirps(end=1201))) # Michael S. Branicky, Jan 24 2021, updated Jul 28 2022

More terms from James Sellers, Jan 22 2000

A074832 Primes whose binary reversal is also prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 97, 101, 107, 113, 127, 131, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 251, 257, 263, 269, 277, 283, 307, 313, 331, 337, 349, 353, 359, 373, 383, 409, 421, 431, 433, 443

Offset: 1

Robert G. Wilson v, Sep 09 2002

By definition, all Mersenne primes are in this sequence. - Roderick MacPhee, Apr 18 2015

			349 = 101011101, reverse the sequence of ones and zeros: 101110101 = 373 which is also prime.

T. D. Noe, Table of n, a(n) for n=1..10000
K. S. Brown's Mathpages, Reflective and Cyclic Sets of Primes
Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, Reversible primes, arXiv:2309.11380 [math.NT], 2023. See p. 3.

Cf. A007500 (primes whose decimal reversal is also prime).

Prime[ Select[ Range[100], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 2]], 2]] &]]

from sympy import isprime, prime
A074832 = [prime(n) for n in range(1,10**6) if isprime(int(bin(prime(n))[:1:-1],2))] # Chai Wah Wu, Aug 14 2014

A061247 Primes having only {0, 1, 8} as digits.

Original entry on oeis.org

11, 101, 181, 811, 881, 1181, 1801, 1811, 8011, 8081, 8101, 8111, 10111, 10181, 11801, 18181, 80111, 81001, 81101, 81181, 88001, 88801, 88811, 100801, 100811, 101081, 101111, 108011, 108881, 110881, 118081, 118801, 180001, 180181, 180811

Offset: 1

Amarnath Murthy, Apr 23 2001

The intersection with A007500 is listed in A199328. - M. F. Hasler, Nov 05 2011

			a(6) = 1801, 1801 is a prime and consists of only 1, 8 and 0.

Robert Israel, Table of n, a(n) for n = 1..17482

Cf. A061246, A020449-A020472, A199325-A199329.

[NthPrime(n): n in [1..2*10^4] | forall{d: d in Intseq(NthPrime(n)) | d in [0, 1, 8]}]; // Vincenzo Librandi, May 15 2019

N:= 1000: # to get the first N entries
count:= 0:
allowed:= {0,1,8}:
nallowed:= nops(allowed):
subst:= seq(i=allowed[i+1],i=0..nallowed-1);
for d from 1 while count < N do
  for x1 from 1 to nallowed-1 while count < N do
    for t from 0 to nallowed^d-1  while count < N do
      L:= subs(subst,convert(x1*nallowed^d+t,base,nallowed));
      X:= add(L[i]*10^(i-1),i=1..d+1);
      if isprime(X) then
          count:= count+1;
          A[count]:= X;
      fi
od od od:
seq(A[n],n=1..N); # Robert Israel, Apr 20 2014

Select[Prime[Range[50000]],Length[Union[{0,1,8},IntegerDigits[ # ]]] == 3&] (* Stefan Steinerberger, Jun 10 2007 *)
Select[FromDigits/@Tuples[{0,1,8},6],PrimeQ] (* Harvey P. Dale, Jan 12 2016 *)

a(n=50, L=[0, 1, 8], show=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1 && !L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u) || next; show && print1(t", "); n-- || return(t)))} \\ M. F. Hasler, Nov 05 2011

Corrected and extended by Stefan Steinerberger, Jun 10 2007

A095179 Numbers whose reversed digit representation is prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 14, 16, 17, 20, 30, 31, 32, 34, 35, 37, 38, 50, 70, 71, 73, 74, 76, 79, 91, 92, 95, 97, 98, 101, 104, 106, 107, 110, 112, 113, 118, 119, 124, 125, 128, 130, 131, 133, 134, 136, 140, 142, 145, 146, 149, 151, 152, 157, 160, 164, 166, 167, 170, 172

Offset: 1

Cino Hilliard, Jun 21 2004

If m is a term, then 10*m is another term. - Bernard Schott, Nov 20 2021

			The number 70 in reverse is 07 = 7, which is prime.

Michael S. Branicky, Table of n, a(n) for n = 1..11018 (all terms < 10**5)

Cf. A004086, A007500 (primes in this sequence), A076055 (composites in this sequence), A204232 (base-2 analog), A097312.

q:= n-> (s-> isprime(parse(cat(s[-i]$i=1..length(s)))))(""||n):
select(q, [$1..200])[];  # Alois P. Heinz, Aug 22 2021

Select[Range[200], PrimeQ[FromDigits[Reverse[IntegerDigits[#]]]] &] (* Harvey P. Dale, Jun 13 2013 *)

r(n) = for(x=1,n,y=eval(rev(x));if(isprime(y),print1(x","))) \ Get the reverse of the input string rev(str) = { local(tmp,j,s); tmp = Vec(Str(str)); s=""; forstep(j=length(tmp),1,-1, s=concat(s,tmp[j])); return(s) }

is_A095179(n)=isprime(eval(Strchr(vecextract(Vec(Vecsmall(Str(n))),"-1..1")))) \\ M. F. Hasler, Jan 13 2012

isok(n) = isprime(fromdigits(Vecrev(digits(n)))); \\ Michel Marcus, Aug 22 2021

from sympy import isprime
def ok(n): return isprime(int(str(n)[::-1]))
print(list(filter(ok, range(1, 173)))) # Michael S. Branicky, Aug 22 2021

Offset corrected to 1 by Alonso del Arte, Apr 12 2020

A046732 "Norep emirps": primes with distinct digits which remain prime when reversed.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 31, 37, 71, 73, 79, 97, 107, 149, 157, 167, 179, 347, 359, 389, 701, 709, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 1069, 1097, 1237, 1249, 1259, 1279, 1283, 1409, 1429, 1439, 1453, 1487, 1523, 1583, 1597, 1657, 1723, 1753

Offset: 1

Enoch Haga

There are no 10-digit terms because their sum of digits would be 45 and thus the number would be divisible by 3.

There are 25332 terms in this sequence, the last of which is 987653201, as found by Harvey P. Dale. - see Martin Gardner's column in Scientific American.

Nathaniel Johnston, Table of n, a(n) for n = 1..25332 (full sequence).
Chris K. Caldwell and G. L. Honaker, Jr., 987653201, Prime Curios!.
Martin Gardner, Patterns in primes are a clue to the strong law of small numbers, Mathematical Games, Scientific American, Vol. 243, No. 4, September, 1980.
Carlos Rivera, Puzzle 59. Six and the nine digits primes (by Jud McCranie), The Prime Puzzles and Problems Connection.

Intersection of A007500 and A029743.

Cf. A006567, A003684, A007628, A048051, A048052, A048053, A048054, A048895.

read(transforms): A046732 := proc(n) option remember: local d,k,p,distdig: if(n=1)then return 2: fi: p:=procname(n-1): do p:=nextprime(p): if(isprime(digrev(p)))then d:=convert(p,base,10): distdig:=true: for k from 0 to 9 do if(numboccur(d,k)>1)then distdig:=false: break: fi: od: if(distdig)then return p: fi: fi: od: end: seq(A046732(n),n=1..52); # Nathaniel Johnston, May 29 2011

Select[Prime[Range[280]], Length[Union[x = IntegerDigits[#]]] == Length[x] && PrimeQ[FromDigits[Reverse[x]]] &] (* Jayanta Basu, Jun 28 2013 *)

from sympy import prime, isprime
A046732 = [p for p in (prime(n) for n in range(1,10**3)) if len(str(p)) == len(set(str(p))) and isprime(int(str(p)[::-1]))] # Chai Wah Wu, Aug 14 2014

More terms from Jud McCranie.

A071786 In prime factorization of n replace each prime with its reversal (in decimal notation).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 14, 15, 16, 71, 18, 91, 20, 21, 22, 32, 24, 25, 62, 27, 28, 92, 30, 13, 32, 33, 142, 35, 36, 73, 182, 93, 40, 14, 42, 34, 44, 45, 64, 74, 48, 49, 50, 213, 124, 35, 54, 55, 56, 273, 184, 95, 60, 16, 26, 63, 64, 155, 66, 76, 284, 96, 70, 17, 72

Offset: 1

Reinhard Zumkeller, Jun 06 2002

The range of A007500 is a subset of the range of this sequence. - Reinhard Zumkeller, Jul 06 2009

Prime factors counted with multiplicity. - Harvey P. Dale, Jul 08 2017

			a(143) = a(11*13) = a(11)*a(13) = 11*31 = 341.

N. J. A. Sloane, Table of n, a(n) for n = 1..10000
Index to divisibility sequences

Cf. A151764, A161594, A151765. For records see A151766, A151767.
Cf. A151768 (complement), A376858 (fixed points).
Cf. A027746.

a071786 = product . map a004086 . a027746_row
-- Reinhard Zumkeller, Oct 14 2011

read("transforms") ; A071786 := proc(n) local ifs, a, d ; ifs := ifactors(n)[2] ; a := 1 ; for d in ifs do a := a*digrev(op(1, d))^op(2, d) ; od: a ; end: # R. J. Mathar, Jun 16 2009
# second Maple program:
r:= n-> (s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||n):
a:= n-> mul(r(i[1])^i[2], i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 19 2017

Table[Times@@IntegerReverse/@Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ n]],{n,80}] (* Harvey P. Dale, Jul 08 2017 *)

rev(n)=fromdigits(Vecrev(digits(n)))
a(n)=my(f=factor(n)); prod(i=1,#f~,rev(f[i,1])^f[i,2]) \\ Charles R Greathouse IV, Jun 28 2015

from sympy import factorint
from operator import mul
from functools import reduce
def A071786(n):
    return 1 if n==1 else reduce(mul,(int(str(p)[::-1])**e for p,e in factorint(n).items())) # Chai Wah Wu, Aug 14 2014

Completely multiplicative with a(p) = A004086(p), p prime.

a(A000040(n)) = A004087(n).

cp's OEIS Frontend

A199305 Palindromic primes in the sense of A007500 with digits '0', '1' and '5' only.

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A002385 Palindromic primes: prime numbers whose decimal expansion is a palindrome.

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A006567 Emirps (primes whose reversal is a different prime).

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A074832 Primes whose binary reversal is also prime.

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A061247 Primes having only {0, 1, 8} as digits.

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A095179 Numbers whose reversed digit representation is prime.

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