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Numbers k such that 6*10^k + 91 is prime.
0

%I #21 Jun 09 2024 18:06:06

%S 0,1,2,3,4,5,7,10,11,14,23,31,37,42,105,106,114,137,182,212,233,313,

%T 621,629,1067,1570,4612,6288,20030,21843,24800,43694,179970

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

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 0 followed by the digits 91 is prime (see Example section).

%C a(34) > 3*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 60w91</a>.

%e 3 is in this sequence because 6*10^3+91 = 6091 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 97;

%e a(2) = 1, 151;

%e a(3) = 2, 691;

%e a(4) = 3, 6091;

%e a(5) = 4, 60091, etc.

%t Select[Range[0, 100000], PrimeQ[6*10^# + 91] &]

%o (PARI) is(n)=ispseudoprime(6*10^n + 91) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,3

%A _Robert Price_, Apr 06 2016

%E a(33) from _Robert Price_, May 21 2019