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Numbers k such that 5*10^k + 59 is prime.
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%I #15 Jun 02 2024 14:03:38

%S 1,3,7,9,10,19,21,22,43,46,58,87,216,549,604,1147,1858,2952,3684,4057,

%T 4246,4354,8212,8289,9013,16968,19107,57754,61348,88254

%N Numbers k such that 5*10^k + 59 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 59 is prime (see Example section).

%C a(31) > 2*10^5.

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

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 50w59</a>.

%e 3 is in this sequence because 5*10^3 + 59 = 5059 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 109;

%e a(2) = 3, 5059;

%e a(3) = 7, 50000059;

%e a(4) = 9, 5000000059;

%e a(5) = 10, 50000000059, etc.

%t Select[Range[0, 100000], PrimeQ[5*10^# + 59] &]

%o (PARI) is(n)=ispseudoprime(5*10^n + 59) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more

%O 1,2

%A _Robert Price_, Sep 05 2016