

A068811


Numbers n such that n and its 10's complement are both primes, i.e., n and 10^k  n where k is the number of digits in n, are primes.


5



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
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OFFSET

1,1


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
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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


EXAMPLE

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 1000641 = 359 are primes.


MATHEMATICA

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


PROG

(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^(d1), 10^d, if(isprime(10^dp), 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


CROSSREFS

Sequence in context: A241896 A076186 A092564 * A088083 A116457 A037155
Adjacent sequences: A068808 A068809 A068810 * A068812 A068813 A068814


KEYWORD

easy,nonn,base


AUTHOR

Amarnath Murthy, Mar 07 2002


EXTENSIONS

Corrected by Jason Earls, May 25 2002
Edited by N. J. A. Sloane, Sep 18 2008 at the suggestion of R. J. Mathar


STATUS

approved



