A159352 - OEIS

%I #13 Jul 07 2023 17:16:55

%S 13,103,100003,1000003,100000000003,100000000000000003,

%T 1000000000000000003,1000000000000000000000000000000000000003,

%U 100000000000000000000000000000000000000000000000000000003

%N Primes of the form "1 [0]_n 3" - with zeros between 1 and 3.

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/10003.htm#prime">Prime numbers of the form 100...003</a>.

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

%e 1000000000000000000000000000000000000003 is a prime with 38 zeros between 1 and 3.

%p select(isprime, [seq(10^k+3, k=1..998)]); # _Robert Israel_, Dec 28 2015

%o (Magma) [p: n in [1..100] | IsPrime(p) where p is 10^n+3 ]; // _Klaus Brockhaus_, Apr 12 2009

%Y Cf. A159031.

%Y Cf. A049054 (numbers n such that 10^n + 3 is prime), A102006 (numbers n such that 10*10^n + 3 is prime), A011557 (powers of 10).

%K base,nonn

%O 1,1

%A _Parthasarathy Nambi_, Apr 11 2009