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%I #14 Apr 09 2024 22:03:23
%S 123457,423457,523459,723451,823451,823457,923453,1234511,1234517,
%T 1234531,1234537,1234543,1234547,1234577,2234501,2234503,2234513,
%U 2234539,2234543,2234549,2234563,2234579,2234587,2234591,2234593,2234597,3234533,3234551,3234599,4234501,4234537,5234513,5234543,5234549
%N Primes whose second, third, fourth and fifth digits are 2345.
%C This sequence is infinite by the Prime Number Theorem. - _Charles R Greathouse IV_, Apr 09 2024
%H Robert Israel, <a href="/A371845/b371845.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ≍ n log n. The ratio a(n)/(n log n) is bounded but does not have a limit. - _Charles R Greathouse IV_, Apr 09 2024
%p R:= NULL: count:= 0:
%p for d from 0 while count < 100 do
%p for a from 1 to 9 while count < 100 do
%p for b from 1 to 10^d-1 by 2 while count < 100 do
%p x:= b + 10^d*(2345 + 10000*a);
%p if isprime(x) then
%p count:= count+1; R:= R, x
%p fi
%p od od od:
%p R;
%t p = 12345; s = {}; Do[p = NextPrime[p];
%t If[2 == IntegerDigits[p][[2]] && 3 == IntegerDigits[p][[3]] && 4 ==IntegerDigits[p][[4]] && 5 == IntegerDigits[p][[5]], AppendTo[s, p]],
%t {1000000}]; s
%o (Python)
%o from itertools import count, islice
%o from sympy import primerange
%o def A371845_gen(): # generator of terms
%o for l in count(1):
%o m = 10**l
%o for a in range(1,10):
%o b = (a*10**4+2345)*m
%o yield from primerange(b,b+m)
%o A371845_list = list(islice(A371845_gen(),20)) # _Chai Wah Wu_, Apr 09 2024
%Y Cf. A371833.
%K nonn,base
%O 1,1
%A _Zak Seidov_ and _Robert Israel_, Apr 08 2024
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