A034844 Primes with only nonprime decimal digits.

11, 19, 41, 61, 89, 101, 109, 149, 181, 191, 199, 401, 409, 419, 449, 461, 491, 499, 601, 619, 641, 661, 691, 809, 811, 881, 911, 919, 941, 991, 1009, 1019, 1049, 1061, 1069, 1091, 1109, 1181, 1409, 1481, 1489, 1499, 1601, 1609, 1619, 1669, 1699, 1801, 1811

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• base

Comments

A109066(n) = 0 iff prime(n) is in this sequence. [Reinhard Zumkeller, Jul 11 2010, corrected by M. F. Hasler, Aug 27 2012]

Or, primes p such that A193238(p) = 0. - M. F. Hasler, Aug 27 2012

Intersection of A084984 and A000040; complement of A179336 (within the primes A000040). [Reinhard Zumkeller, Jul 19 2011, edited by M. F. Hasler, Aug 27 2012]

The smallest prime that contains all the six nonprime decimal digits is a(694) = 104869 (see Prime Curios! link). - Bernard Schott, Mar 21 2023

Examples

			E.g. 149 is a prime made of nonprime digits(1,4,9).
991 is a prime without any prime digits.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Chris Caldwell, The First 1,000 Primes
• Chris K. Caldwell and G. L. Honaker, Jr., 104869, Prime Curios!

Crossrefs

Cf. A000040, A084984.

Cf. A033274, A109066, A152313, A141409.

Programs

Haskell

a034844 n = a034844_list !! (n-1)
a034844_list = filter (not . any  (`elem` "2357") . show ) a000040_list
-- Reinhard Zumkeller, Jul 19 2011

Magma

[p: p in PrimesUpTo(2000) | forall{d: d in [2,3,5,7] | d notin Set(Intseq(p))}];  // Bruno Berselli, Jul 27 2011

Mathematica

Select[Prime[Range[279]], Intersection[IntegerDigits[#], {2, 3, 5, 7}] == {} &] (* Jayanta Basu, Apr 18 2013 *)
Union[Select[Flatten[Table[FromDigits/@Tuples[{1,4,6,8,9,0},n],{n,2,4}]],PrimeQ]] (* Harvey P. Dale, Dec 08 2014 *)

PARI

is_A034844(n)=isprime(n)&!apply(x->isprime(x),eval(Vec(Str(n)))) \\ M. F. Hasler, Aug 27 2012

PARI

is_A034844(n)=isprime(n)&!setintersect(Set(Vec(Str(n))),Vec("2357")) \\ M. F. Hasler, Aug 27 2012

Python

from sympy import isprime
from itertools import product
def auptod(maxdigits):
    alst = []
    for d in range(1, maxdigits+1):
        for p in product("014689", repeat=d-1):
            if d > 1 and p[0] == "0": continue
            for end in "19":
                s = "".join(p) + end
                t = int(s)
                if isprime(t): alst.append(t)
    return alst
print(auptod(4)) # Michael S. Branicky, Nov 19 2021

Formula

a(n) >> n^1.285. [Charles R Greathouse IV, Feb 20 2012]

Extensions

Edited by N. J. A. Sloane, Feb 22 2009 at the suggestion of R. J. Mathar