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

1,1

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

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!

Formula

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A000040, A084984.

Cf. A033274, A109066, A152313, A141409.

Sequence in context: A081027 A322474 A084986 * A092627 A152313 A034303

Adjacent sequences: A034841 A034842 A034843 * A034845 A034846 A034847

Keyword

nonn,base

Author

Erich Friedman

Extensions

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

Status

approved