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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

%I

%S 3,5,7,11,17,29,41,47,53,59,71,83,89,97,113,137,173,179,191,227,239,

%T 257,281,317,347,353,359,383,401,431,443,479,491,509,521,557,569,599,

%U 617,641,647,653,683,719,743,761,773,809,821,827,863,887,911,929,941

%N 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.

%C 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

%C 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

%H Vincenzo Librandi, <a href="/A068811/b068811.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%e 641 is a term as 641 and 1000-641 = 359 are primes.

%t Select[Prime[Range[160]], PrimeQ[10^(Floor[Log[10, # ]] + 1) - # ] &] (* _Stefan Steinerberger_, Jun 15 2007 *)

%o (PARI) is_A068811(p)= isprime(10^#Str(p)-p) & isprime(p) \\ _M. F. Hasler_, May 01 2012

%o (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

%o (Sage) [p for p in prime_range(100) if is_prime(10^p.ndigits()-p)] # _Giuseppe Coppoletta_, Jul 24 2016

%K easy,nonn,base

%O 1,1

%A _Amarnath Murthy_, Mar 07 2002

%E Corrected by _Jason Earls_, May 25 2002

%E Edited by _N. J. A. Sloane_, Sep 18 2008 at the suggestion of _R. J. Mathar_

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Last modified August 3 21:09 EDT 2021. Contains 346441 sequences. (Running on oeis4.)