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Numbers k such that 10^k + 7 is prime.
23

%I #67 Apr 03 2023 10:36:10

%S 1,2,4,8,9,24,60,110,134,222,412,700,999,1383,5076,5543,6344,14600,

%T 15093,21717,23636,30221,50711,221628,350071,371696,487291,995256,

%U 1043372

%N Numbers k such that 10^k + 7 is prime.

%C No other terms less than 59500.

%C No other terms <= 100000. - _Robert Price_, Mar 03 2011

%C a(28) > 500000. - _Alfred Reich_, Jun 10 2021

%C a(29) > 1000000. - _Alfred Reich_, Nov 20 2021

%C a(30) > 1075000. - _Alfred Reich_, Jan 10 2022

%H G. L. Honaker, Jr. and Chris Caldwell, eds., <a href="https://t5k.org/curios/page.php/1000000007.html">Prime Curios!</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/10007.htm#prime">Prime numbers of the form 100...007</a>.

%H Alfred Reich, <a href="https://www.alfredreichlg.de/10w7/prp/ProofFile.200001-1000000.txt">ProofFile</a>.

%H Alfred Reich, <a href="https://www.alfredreichlg.de/10w7/prp/ProofFile.1000001-1075000.txt">ProofFile2</a>.

%H Sabin Tabirca and Kieran Reynolds, <a href="http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>.

%F a(n) = A102007(n) + 1.

%e 8 is a term since 10^8 + 7 = 100000007 is a prime.

%t Do[ If[ PrimeQ[ 10^n + 7], Print[n]], {n, 0, 10000}] (* _Robert G. Wilson v_, Dec 16 2004 *)

%o (PARI) is(n)=isprime(10^n + 7) \\ _Charles R Greathouse IV_, Apr 29 2015

%Y Cf. A088275, A049054, A102007, A159031.

%K nonn,more

%O 1,2

%A _Amarnath Murthy_, Sep 28 2003

%E a(7)-a(14) from _Ray Chandler_, Oct 09 2003

%E a(15)-a(19) from _Robert G. Wilson v_, Jan 18 2005

%E Corrected and extended by _Jason Earls_, Nov 27 2007 and Dec 07 2007. (14600 was missing and 23636 and 50711 are new. These are presently only probable primes, found with WinPFGW.)

%E Missing term 30221 added by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(24)-a(27) from _Alfred Reich_, Jun 10 2021

%E a(28) from _Alfred Reich_, Nov 20 2021

%E a(29) from _Alfred Reich_, Jan 10 2022