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.
The reverse of prime 9387802769 is 9672087839 is also prime, as are all of these numbers.
f[n_] := Block[{k = 10^(n - 1)}, While[ !PrimeQ[k] || !PrimeQ[FromDigits@Reverse@IntegerDigits@k], k++ ]; k]; Array[f, 19] (* Robert G. Wilson v, Nov 19 2005 *)
lndp[n_]:=Module[{p=NextPrime[10^n]},While[CompositeQ[IntegerReverse[ p]],p = NextPrime[ p]];p]; Array[lndp,20,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 05 2019 *)
for(x=1,1e99, until( isprime(x=nextprime(x+1)) & isprime(eval(concat(vecextract(Vec(Str(x)),"-1..1")))),); print1(x", "); x=10^#Str(x)-1) \\ M. F. Hasler, Nov 21 2009
from sympy import isprime def c(n): return isprime(n) and isprime(int(str(n)[::-1])) def a(n): return next(p for p in range(10**(n-1), 10**n) if c(p)) print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jun 27 2022
Select[Prime@Range[10^4], # != IntegerReverse[ # ] && PrimeQ[IntegerReverse[ # ]] && Intersection[IntegerDigits[ # ], {0, 1, 4, 6, 8, 9}] == {} &] (* Ray Chandler, Mar 06 2007; corrected by James C. McMahon, Jun 03 2025 *)
Table[Select[FromDigits/@Tuples[{2,3,5,7},n],!PalindromeQ[#]&& AllTrue[ {#, IntegerReverse[ #]},PrimeQ]&],{n,2,5}]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 17 2019 *)
a(2)= 1207 = 17 * 71.
revdigs:= proc(n) local i,L; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc: f:= proc(p) local r; if not isprime(p) then return NULL fi; r:= revdigs(p); if r > p and isprime(r) then r*p fi end proc: sort(map(f, [seq(i,i=13..9999,2)])); # Robert Israel, Dec 26 2018
dr[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Select[Prime[Range[1000]], PrimeQ[dr[ # ]]&&dr[ # ]<#&] Select[Prime[Range[600]],PrimeQ[IntegerReverse[#]]&&#>IntegerReverse[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 23 2020 *)
a(2) = 31 because of the four consecutive primes 29, 31, 37, 41 only 31, 37 are emirps.
from sympy import isprime, nextprime
def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))
def aupto(limit):
alst, pvec, evec, p = [], [2, 3, 5, 7], [0, 0, 0, 0], 11
while pvec[1] <= limit:
if evec == [0, 1, 1, 0]: alst.append(pvec[1])
pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]; p = nextprime(p)
return alst
print(aupto(12689)) # Michael S. Branicky, Jul 04 2021
A000040(10) = 29 -> '11101' rev '10111' -> 23 = A000040(9), therefore 29 and 23 are terms. The prime 19 is not a term, as 19 -> '10011' rev '11001' -> 25 = 5^2; and 7 = A074832(3) is not a term because it is a binary palindrome (A006995) and therefore not different.
revdigs:= proc(n) local L; L:= convert(n,base,2); add(L[-i]*2^(i-1),i=1..nops(L)) end proc: filter:= proc(t) local r; if not isprime(t) then return false fi; r:= revdigs(t); r <> t and isprime(r) end proc: select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Aug 30 2016
Select[Prime[Range[100]], (r = IntegerReverse[#, 2]) != # && PrimeQ[r] &] (* Amiram Eldar, Jul 28 2025 *)
from sympy import isprime
def ok(n):
r = int(bin(n)[2:][::-1], 2)
return n != r and isprime(n) and isprime(r)
print([k for k in range(600) if ok(k)]) # Michael S. Branicky, Jul 30 2022
a(1) = 71 because of the five consecutive primes 67, 71, 73, 79, 83 all except 67 and 83 are emirps and this is the first such occurrence.
Select[Prime@Range@10000,Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#,Range[-1,3]])]=={0,1,1,1,0}&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)
from sympy import isprime, primerange
def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))
def aupto(limit):
alst, pvec, evec = [], [2, 3, 5, 7, 11], [0, 0, 0, 0, 0]
for p in primerange(13, limit+1):
if evec == [0, 1, 1, 1, 0]: alst.append(pvec[1])
pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]
return alst
print(aupto(20000)) # Michael S. Branicky, Jul 04 2021
a(1) = 733 because of the six consecutive primes 727, 733, 739, 743, 751, 757 all except 727 and 757 are emirps and this is the first such occurrence.
Select[Prime@Range@10000,Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#,Range[-1,4]])]=={0,1,1,1,1,0}&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)
from sympy import isprime, primerange
def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))
def aupto(limit):
alst, pvec, evec = [], [2, 3, 5, 7, 11, 13], [0, 0, 0, 0, 0, 0]
for p in primerange(17, limit+1):
if evec == [0, 1, 1, 1, 1, 0]: alst.append(pvec[1])
pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]
return alst
print(aupto(97000)) # Michael S. Branicky, Jul 04 2021
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