%I #42 May 03 2024 12:38:19

%S 0,1,2,3,13,229,242,309,957,1473,1494,3182,3727,4177,23210,25719,

%T 32835,36990,103958,789955,1038890

%N Numbers n such that 4*10^n + 1 is prime.

%C Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - _Hugo Pfoertner_, Nov 14 2019

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/4/40001.htm#prime">Prime numbers of the form 400...001</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) = A101712(n-1) + 1.

%t Do[ If[ PrimeQ[ 4*10^n + 1], Print[ n ]], {n, 0, 30000}]

%o (PARI) is(n)=isprime(4*10^n+1) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A056797 (9*10^n+1 is prime), A101712.

%K more,nonn

%O 1,3

%A _Robert G. Wilson v_, Aug 22 2000

%E a(12)-a(16) using PrimeForm from _Hugo Pfoertner_, Jul 08 2004

%E 32835 from _Ray Chandler_, Aug 30 2010

%E 36990 from Peter Benson, Aug 23 2003 confirmed as next term by _Ray Chandler_, Sep 07 2010

%E 103958 from Peter Benson, Dec 31 2004 confirmed as next term by _Ray Chandler_, Feb 18 2012

%E a(20)-a(21) from Kamada data by _Tyler Busby_, May 03 2024