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A108050 Integers k such that 10^k+21 is prime.

%I A108050 #52 Jul 06 2025 14:58:44
%S A108050 1,3,9,17,55,77,133,195,357,1537,2629,3409,8007,25671,48003,55811,
%T A108050 94983,109615,135669
%N A108050 Integers k such that 10^k+21 is prime.
%C A108050 There cannot be any primes of this form when k is even, because all such numbers must be divisible by 11. A number is divisible by 11 if the difference between the sum of its odd digits and the sum of its even digits is 0 or divisible by 11. When k is even, the difference is always 0. - _Dmitry Kamenetsky_, Jul 12 2008
%C A108050 The next term, if one exists, is >100000. - _Robert Price_, Mar 24 2011
%C A108050 See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10021".
%H A108050 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/">List of near-repdigit-related prime numbers</a>
%H A108050 Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=10%5Ek%2B21">Search for 10^k+21</a>, PRP Top Records.
%H A108050 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%e A108050 For k=3 we have 10^3+21 = 1000+21 = 1021, which is prime.
%t A108050 q=21; s=""; For[ a=q,a<=q,s="10^n+"<>ToString[ a ]<>":"; n=0; For[ i=1,i< 10^3,If[ PrimeQ[ 10^i+a ],n=1; s=s<>ToString[ i ]<>"," ]; i++ ]; If[ n>0,Print[ s ] ]; a++ ] (* _Vladimir Joseph Stephan Orlovsky_, May 06 2008 *)
%o A108050 (PARI) for(n=1,1e4,if(ispseudoprime(10^n+21),print1(n", "))) \\ _Charles R Greathouse IV_, Jul 20 2011
%Y A108050 Cf. A049054, A088274, A088275, A138861.
%K A108050 more,nonn
%O A108050 1,2
%A A108050 Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005
%E A108050 a(6)=77 inserted by _Vladimir Joseph Stephan Orlovsky_, May 06 2008
%E A108050 a(13)=8007 from _Dmitry Kamenetsky_, Jul 12 2008
%E A108050 a(14)=25671 from _Robert Price_, Nov 08 2010
%E A108050 Edited by _Ray Chandler_, Dec 24 2010
%E A108050 a(15)=48003 from _Robert Price_, Dec 31 2010
%E A108050 a(16)=55811 from _Robert Price_, Jan 09 2011
%E A108050 a(17)=94983 from _Robert Price_, Mar 24 2011
%E A108050 a(18)=109615 from Lelio R Paula, added by _Boyan Hu_, Jul 05 2025
%E A108050 a(19)=135669 from _Boyan Hu_, Jul 05 2025