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URL: https://oeis.org/A088275

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A088275
Numbers k such that 10^k + 9 is prime.
26
1, 2, 3, 4, 9, 18, 22, 45, 49, 56, 69, 146, 202, 272, 2730, 2841, 4562, 31810, 43186, 48109, 92691, 237670, 400310, 482706, 831776, 1036183
OFFSET
1,2
COMMENTS
No others less than 9000. - Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
No others less than 39254. - Dirk Augustin, Oct 24 2006
2730, 2841 and 4562 all give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005
Verified existing terms. No other terms less than 40001. - Robert Price, Aug 14 2010
No other terms <= 100000. - Robert Price, Mar 03 2011
a(23) > 3*10^5. - Robert Price, Oct 26 2023
a(27) > 1.1*10^6. - Boyan Hu, Mar 21 2026
LINKS
Henri Lifchitz and Renaud Lifchitz (Editors), Search for 10^k+9, PRP Top Records.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers, Smarandache Notions Journal, 2003.
FORMULA
a(n) = A102008(n) + 1.
EXAMPLE
4 is a term since 10^4 + 9 = 10009 is a prime.
5 is not a term since 10^5 + 9 = 100009 = 7^2*13*157 is not a prime.
MATHEMATICA
Do[ If[ PrimeQ[ 10^n + 9], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 16 2004 *)
PROG
(PARI) is(n)=isprime(10^n + 9) \\ Charles R Greathouse IV, Apr 29 2015
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Amarnath Murthy, Sep 28 2003
EXTENSIONS
a(8)-a(16) from Ray Chandler, Oct 10 2003
a(17) from Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
a(18) (a PRP) found by Dirk Augustin, Oct 16 2006
a(19)-a(20) (probable primes), found with WinPFGW. No others less than 60400. - Jason Earls, Dec 22 2007
a(21) from Robert Price, Mar 03 2011
a(22) from Robert Price, Oct 26 2023
a(23) from Boyan Hu, Jun 15 2025
a(24) from Boyan Hu, Jun 24 2025
a(25) from Boyan Hu, Dec 19 2025
a(26) from Boyan Hu, Feb 21 2026
STATUS
approved