A097970 - OEIS

%I #31 Sep 08 2022 08:45:14

%S 1,4,6,16,22,39,103,163,240,1048,1974,2559,5880,14436,28338,32796,

%T 38079,56779,91215,111325,115863,138604

%N Numbers n such that 7*10^n + 3 is prime.

%C a(23) > 2*10^5. - _Robert Price_, Aug 15 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/70003.htm#prime">Prime numbers of the form 700...003</a>.

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

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A101129(n) + 1.

%e For n = 1 we have 7*10^1+3 =7*10+3 = 73, which is prime.

%t Do[ If[ PrimeQ[ 7*10^n + 3], Print[ n ]], {n, 0, 10000}] (* _Robert G. Wilson v_, Jan 19 2005 *)

%t Flatten[Position[Table[7 10^n+3,{n,100000}],_?PrimeQ]] (* _Harvey P. Dale_, Nov 01 2011 *)

%t Select[Range[15000], PrimeQ[7 10^# + 3] &] (* _Vincenzo Librandi_, Aug 16 2015 *)

%o (PARI) main(m)=select(n->isprime(7*10^n + 3),vector(m,i,i)) \\ _Anders Hellström_, Aug 15 2015

%o (Magma) [n: n in [0..500] | IsPrime(7*10^n + 3)]; // _Vincenzo Librandi_, Aug 16 2015

%Y Cf. A101129.

%K more,nonn

%O 1,2

%A Julien Peter Benney (jpbenney(AT)ftml.net), Sep 07 2004

%E a(10)-a(13) from _Robert G. Wilson v_, Jan 19 2005

%E a(14)-a(19) from Kamada data by _Robert Price_, Dec 14 2010

%E a(20)-a(22) from _Robert Price_, Aug 15 2015