A081677 - OEIS

%I #34 Sep 08 2022 08:45:09

%S 0,1,3,5,6,7,12,16,17,22,24,35,115,120,358,1488,1819,4679,9821,27217,

%T 27693,194413

%N Numbers n such that 2*10^n + 3 is prime.

%C a(22) > 10^5. - _Robert Price_, Nov 16 2014

%C a(23) > 2*10^5. - _Robert Price_, Jul 11 2015

%D Mark A. Herkommer, Number Theory, A Programmer's Guide, McGraw-Hill, New York, 1999, page 51.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/20003.htm#prime">Prime numbers of the form 200...003</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) = A101951(n-1) + 1.

%e 2+3 is prime, so are 23, 2003, 200003, 2000003, 20000003,2000000000003, etc. which are all of the form 2*10^n +3.

%t Do[ If[ PrimeQ[2*10^n + 3], Print[n]], {n, 0, 10000}]

%t Select[Range[0, 1000], PrimeQ[(2 10^# + 3)] &] (* _Vincenzo Librandi_, Nov 17 2014 *)

%o (Magma) [n: n in [0..500] | IsPrime(2*10^n+3)]; // _Vincenzo Librandi_, Nov 17 2014

%o (PARI) is(n)=isprime(2*10^n+3) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A101951.

%K more,nonn

%O 1,3

%A _Robert G. Wilson v_, Mar 26 2003

%E More terms from _Robert G. Wilson v_, Jan 18 2005

%E a(20)-a(21) from Kamada data by _Robert Price_, Dec 09 2010

%E a(22) from _Robert Price_, Jul 11 2015