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A034844
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Primes with only nonprime decimal digits.
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42
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The smallest prime that contains all the six nonprime decimal digits is a(694) = 104869 (see Prime Curios! link). - Bernard Schott, Mar 21 2023
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LINKS
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Chris K. Caldwell and G. L. Honaker, Jr., 104869, Prime Curios!
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FORMULA
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EXAMPLE
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E.g. 149 is a prime made of nonprime digits(1,4,9).
991 is a prime without any prime digits.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a034844 n = a034844_list !! (n-1)
a034844_list = filter (not . any (`elem` "2357") . show ) a000040_list
(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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