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Numbers k such that 7*10^k + 19 is prime.
1

%I #29 Apr 15 2024 03:15:21

%S 1,2,3,4,27,32,63,69,107,145,154,173,190,271,412,1219,1509,2392,4444,

%T 5567,7424,32174,51573

%N Numbers k such that 7*10^k + 19 is prime.

%C No term is divisible by 6 (A047253) because 7*1000000^k + 19 = 7*(76923*13 + 1)^k + 19 is divisible by 13 and is therefore not prime. - _Bruno Berselli_, Jul 05 2016

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w19</a>.

%e 3 is in this sequence because 7*10^3 + 19 = 7019 is prime.

%e 5 is not in the sequence because 7*10^5 + 19 = 79*8861.

%e Initial terms and associated primes:

%e a(1) = 1: 89;

%e a(2) = 2: 719;

%e a(3) = 3: 7019;

%e a(4) = 4: 70019, etc.

%t Select[Range[0, 3000], PrimeQ[7 10^# + 19] &]

%o (Magma) [n: n in [1..800] | IsPrime(7*10^n+19)];

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+19), print1(n, ", "))); \\ _Altug Alkan_, Jul 05 2016

%o (Python)

%o from sympy import isprime

%o def afind(limit, startk=0):

%o sevenpow10 = 7*10**startk

%o for k in range(startk, limit+1):

%o if isprime(sevenpow10 + 19):

%o print(k, end=", ")

%o k += 1

%o sevenpow10 *= 10

%o afind(500) # _Michael S. Branicky_, Dec 31 2021

%Y Subsequence of A047253.

%Y Cf. similar sequences listed in A274676.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Jul 04 2016

%E a(20)-a(21) from _Michael S. Branicky_, Dec 31 2021

%E a(22)-a(23) from Kamada data by _Tyler Busby_, Apr 14 2024