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

Author

Cino Hilliard, Aug 06 2006

Keywords

• base
• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A000040, A124888.

Programs

Mathematica

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

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

Python

from sympy import primepi, primerange
def A272441(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum(primepi(min(x,(1<Chai Wah Wu, Feb 03 2025

Extensions

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