A068811 Numbers k such that k and its 10's complement (10^d-k, where d is the number of digits in k) are both primes.

3, 5, 7, 11, 17, 29, 41, 47, 53, 59, 71, 83, 89, 97, 113, 137, 173, 179, 191, 227, 239, 257, 281, 317, 347, 353, 359, 383, 401, 431, 443, 479, 491, 509, 521, 557, 569, 599, 617, 641, 647, 653, 683, 719, 743, 761, 773, 809, 821, 827, 863, 887, 911, 929, 941

Offset: 1

Author

Amarnath Murthy, Mar 07 2002

Keywords

• easy
• nonn
• base

Comments

In other words, primes p such that the difference between the smallest power of 10 exceeding p and p is prime. - Zak Seidov, Feb 27 2004

a(n) = 10^d - A145985(n), where d is the number of digits in A145985(n). - N. J. A. Sloane, Dec 18 2022

The only twin prime pairs in the sequence are (3,5) and (5,7). This is easily seen by mod 6 congruences using 10^k = 4 (mod 6). - Giuseppe Coppoletta, Jul 24 2016

Examples

			47 is a prime; the smallest power of 10 exceeding 47 is 100 and 100 - 47 = 53 is prime. Therefore 47 is in the sequence.
641 is a term as 641 and 1000-641 = 359 are primes.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 1000 terms from Vincenzo Librandi]

Crossrefs

Cf. A145985.

Programs

Maple

a:=[];
for i from 1 to 1000 do
p:=ithprime(i); d:=length(p); q:=10^d-p;
if isprime(q) then a:=[op(a),p]; fi; od:
a; # N. J. A. Sloane, Dec 18 2022

Mathematica

Select[Prime[Range[160]], PrimeQ[10^(Floor[Log[10, # ]] + 1) - # ] &] (* Stefan Steinerberger, Jun 15 2007 *)

PARI

is_A068811(p)= isprime(10^#Str(p)-p) & isprime(p) \\ M. F. Hasler, May 01 2012

PARI

for(d=1, 4, forprime(p=10^(d-1), 10^d, if(isprime(10^d-p), print1(p", ")))) \\ Charles R Greathouse IV, May 01 2012

Sage

[p for p in prime_range(100) if is_prime(10^p.ndigits()-p)] # Giuseppe Coppoletta, Jul 24 2016

Extensions

Corrected by Jason Earls, May 25 2002

Edited by N. J. A. Sloane, Sep 18 2008 at the suggestion of R. J. Mathar