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Primes of the form "1 [0]_n 7" - with zeros between 1 and 7.
12

%I #16 Jul 07 2023 18:35:45

%S 17,107,10007,100000007,1000000007,1000000000000000000000007,

%T 1000000000000000000000000000000000000000000000000000000000007

%N Primes of the form "1 [0]_n 7" - with zeros between 1 and 7.

%C The next term, a(8), has 111 digits. - _Harvey P. Dale_, Nov 12 2011

%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/1/10007.htm#prime">Prime numbers of the form 100...007</a>.

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

%e 1000000000000000000000007 is a prime with 23 zeros between 1 and 7.

%t Do[ If[ PrimeQ[10^n + 7], Print[10^n + 7]], {n, 100}] (* _Robert G. Wilson v_, Apr 05 2009 *)

%t Select[Table[FromDigits[Join[{1},PadRight[{},n,0],{7}]],{n,0,120}],PrimeQ] (* _Harvey P. Dale_, Nov 12 2011 *)

%Y Cf. A088274. - _Robert G. Wilson v_, Apr 05 2009

%K nonn,base

%O 1,1

%A _Parthasarathy Nambi_, Apr 02 2009

%E a(7) from _Robert G. Wilson v_, Apr 05 2009