A120533 Primes having a prime number of digits.

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283

Offset

1,1

Comments

Before the 20th century, this sequence would have contained the numbers 1,2,3,5,7; see A008578.

There are a total of 8527 terms for primes with 2, 3, or 5 digits, and a total of 594608 terms if primes with 7 digits are also included. - Harvey P. Dale, Nov 02 2020

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..10000

Example

10007 is a 5-digit prime and so belongs to the sequence.

Mathematica

Table[Prime[Range[PrimePi[10^(p-1)]+1, PrimePi[10^p]]], {p, Prime[Range[ 3]]}]//Flatten (* Harvey P. Dale, Nov 02 2020 *)

Prog

(PARI) g(n) = forprime(x=11, n, if(isprime(length(Str(x))), print1(x", ")))
(PARI) forprime(p=2, 5, forprime(q=10^(p-1), 10^p, print1(q", "))) \\ Charles R Greathouse IV, Oct 04 2011
(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    d = 2
    while True:
        yield from (i for i in range(10**(d-1)+1, 10**d, 2) if isprime(i))
        d = nextprime(d)
print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 27 2023

Crossrefs

Cf. A000040, A124888.

Sequence in context: A096489 A008364 A140461 * A226108 A273906 A095862

Adjacent sequences: A120530 A120531 A120532 * A120534 A120535 A120536

Keyword

base,nonn

Author

Cino Hilliard, Aug 06 2006

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 21 2007

Status

approved