cp's OEIS Frontend

A088275 Numbers k such that 10^k + 9 is prime.

%I A088275 #63 Jun 25 2025 10:33:27
%S A088275 1,2,3,4,9,18,22,45,49,56,69,146,202,272,2730,2841,4562,31810,43186,
%T A088275 48109,92691,237670,400310,482706
%N A088275 Numbers k such that 10^k + 9 is prime.
%C A088275 No others less than 9000. - Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
%C A088275 No others less than 39254. - Dirk Augustin, Oct 24 2006
%C A088275 2730, 2841 and 4562 all give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005
%C A088275 Verified existing terms. No other terms less than 40001. - _Robert Price_, Aug 14 2010
%C A088275 No other terms <= 100000. - _Robert Price_, Mar 03 2011
%C A088275 a(23) > 3*10^5. - _Robert Price_, Oct 26 2023
%H A088275 Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=10%5Ek%2B9">Search for 10^k+9</a>, PRP Top Records.
%H A088275 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/10009.htm#prime">Prime numbers of the form 100...009</a>.
%H A088275 Sabin Tabirca and Kieran Reynolds, <a href="https://web.archive.org/web/20150901000000*/http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>, Smarandache Notions Journal, 2003.
%F A088275 a(n) = A102008(n) + 1.
%e A088275 4 is a member since 10^4 + 9 = 10009 is a prime.
%t A088275 Do[ If[ PrimeQ[ 10^n + 9], Print[n]], {n, 0, 10000}] (* _Robert G. Wilson v_, Dec 16 2004 *)
%o A088275 (PARI) is(n)=isprime(10^n + 9) \\ _Charles R Greathouse IV_, Apr 29 2015
%Y A088275 Cf. A049054, A088274, A102008.
%K A088275 nonn,hard,more
%O A088275 1,2
%A A088275 _Amarnath Murthy_, Sep 28 2003
%E A088275 a(8)-a(16) from _Ray Chandler_, Oct 10 2003
%E A088275 a(17) from Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
%E A088275 a(18) (a PRP) found by Dirk Augustin, Oct 16 2006
%E A088275 a(19)-a(20) (probable primes), found with WinPFGW. No others less than 60400. - _Jason Earls_, Dec 22 2007
%E A088275 a(21) from _Robert Price_, Mar 03 2011
%E A088275 a(22) from _Robert Price_, Oct 26 2023
%E A088275 a(23) from _Boyan Hu_, Jun 15 2025
%E A088275 a(24) from _Boyan Hu_, Jun 24 2025