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Numbers k such that 6*10^k - 91 is prime.
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%I #22 May 11 2024 19:24:54

%S 2,6,25,30,45,98,296,498,627,1001,1995,1998,2518,3208,3753,4130,7159,

%T 7660,10840,16187,24744,28345,31499,32999,44838,60959,88938,209846

%N Numbers k such that 6*10^k - 91 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 9 followed by the digits 09 is prime (see Example section).

%C a(29) > 3*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 59w09</a>.

%e 2 is in this sequence because 6*10^2 - 91 = 509 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 509;

%e a(2) = 6, 5999909;

%e a(3) = 25, 59999999999999999999999909;

%e a(4) = 30, 5999999999999999999999999999909;

%e a(5) = 45, 5999999999999999999999999999999999999999999909; etc.

%t Select[Range[2, 100000], PrimeQ[6*10^# - 91] &]

%o (PARI) isok(k) = isprime(6*10^k - 91); \\ _Michel Marcus_, Nov 12 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 11 2017

%E Terms reordered into ascending order by _Robert Price_, Apr 03 2022

%E a(28) from _Robert Price_, Jul 12 2023