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Integers k such that 10^k + 63 is a prime number.
1

%I #25 Jan 25 2022 08:46:28

%S 1,2,3,11,12,37,42,64,101,131,170,366,404,771,1454,1696,4415,5208,

%T 9027,10978,11264,11651,14432,20655,28220,34623,62523,63986

%N Integers k such that 10^k + 63 is a prime number.

%C If another term exists it is > 100000. - _Robert Price_, Apr 25 2011

%C See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10063".

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/">List of near-repdigit-related prime numbers</a>.

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

%e 3 is a term because 10^3 + 63 = 1000 + 63 = 1063, which is prime.

%t Select[Range[2000],PrimeQ[10^#+63]&] (* _Harvey P. Dale_, Jul 24 2009 *)

%Y Cf. A095688, A108052, A108050, A108312, A107083, A108049, A108054.

%K nonn,more

%O 1,2

%A Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008

%E Two additional terms from _Harvey P. Dale_, Jul 24 2009

%E One more term from _Robert Price_, Mar 22 2010

%E Eight more terms from _Robert Price_, Aug 14 2010

%E Edited by _Ray Chandler_, Dec 23 2010

%E a(27)=62523, a(28)=63986 from _Robert Price_, Jan 29 2011