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Integers k such that 7*10^k + 31 is a prime number.
1

%I #28 Sep 08 2022 08:45:20

%S 1,8,11,143,203,2727,2911,3339,17039

%N Integers k such that 7*10^k + 31 is a prime number.

%C See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "70031".

%C a(10) > 10^5. - _Robert Price_, Jan 28 2017

%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 k = 11 is a term because 7*10^11 + 31 = 7*100000000000 + 31 = 700000000000 + 31 = 700000000031, which is a prime.

%t Select[Range[0, 10000], PrimeQ[7 10^# + 31] &] (* _Vincenzo Librandi_, Jul 03 2016 *)

%o (Magma) [n: n in [1..300] | IsPrime(7*10^n+31)]; // _Vincenzo Librandi_, Jul 03 2016

%Y Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054, A110980.

%K nonn,more

%O 1,2

%A Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

%E a(9) from _Ray Chandler_, Dec 23 2010

%E a(1) = 1 prepended by _Vincenzo Librandi_, Jul 03 2016