A371845 Primes whose second, third, fourth and fifth digits are 2345.

123457, 423457, 523459, 723451, 823451, 823457, 923453, 1234511, 1234517, 1234531, 1234537, 1234543, 1234547, 1234577, 2234501, 2234503, 2234513, 2234539, 2234543, 2234549, 2234563, 2234579, 2234587, 2234591, 2234593, 2234597, 3234533, 3234551, 3234599, 4234501, 4234537, 5234513, 5234543, 5234549

Offset

1,1

Comments

This sequence is infinite by the Prime Number Theorem. - Charles R Greathouse IV, Apr 09 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

Maple

R:= NULL: count:= 0:
for d from 0 while count < 100 do
  for a from 1 to 9 while count < 100 do
    for b from 1 to 10^d-1 by 2 while count < 100 do
      x:= b + 10^d*(2345 + 10000*a);
      if isprime(x) then
         count:= count+1; R:= R, x
      fi
od od od:
R;

Mathematica

p = 12345; s = {}; Do[p = NextPrime[p];
If[2 == IntegerDigits[p][[2]] && 3 == IntegerDigits[p][[3]] && 4 ==IntegerDigits[p][[4]] && 5 == IntegerDigits[p][[5]], AppendTo[s, p]],
{1000000}]; s

Prog

(Python)
from itertools import count, islice
from sympy import primerange
def A371845_gen(): # generator of terms
    for l in count(1):
        m = 10**l
        for a in range(1, 10):
            b = (a*10**4+2345)*m
            yield from primerange(b, b+m)
A371845_list = list(islice(A371845_gen(), 20)) # Chai Wah Wu, Apr 09 2024

Crossrefs

Cf. A371833.

Sequence in context: A178476 A104973 A077301 * A209734 A049358 A245682

Adjacent sequences: A371842 A371843 A371844 * A371846 A371847 A371848

Keyword

nonn,base

Author

Zak Seidov and Robert Israel, Apr 08 2024

Status

approved