A152313 -id:A152313 - cp's OEIS frontend

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

Erich Friedman

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

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

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!

Cf. A000040, A084984.

Cf. A033274, A109066, A152313, A141409.

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

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

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 *)

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

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

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

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

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

A051416 Primes whose digits are composite; primes having only {4, 6, 8, 9} as digits.

Original entry on oeis.org

89, 449, 499, 4649, 4889, 4969, 4999, 6449, 6469, 6689, 6869, 6899, 6949, 8669, 8689, 8699, 8849, 8969, 8999, 9649, 9689, 9949, 44449, 44699, 46489, 46499, 46649, 46889, 48449, 48649, 48869, 48889, 48989, 49499, 49669, 49999, 64489, 64499, 64849, 64969, 66449

Offset: 1

G. L. Honaker, Jr., Jan 17 2000

Primes formed by using only digits 4, 6, 8, 9. Of course, all the terms of this sequence end with 9. - Bernard Schott, Jan 31 2019

			89 is the smallest composite-digit prime and also the only composite-digit prime whose digits are distinct. - _Bernard Schott_, Jan 31 2019

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Chris Caldwell, The Prime Glossary, Composite number
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 89
Index to entries for primes with digits in a given set

Cf. A019546 (with prime digits), A030096 (with odd digits), A061246 (with square digits), A061371 (composite numbers with prime digits).

Subsequence of A061372 and of A152313.

Select[Prime@Range[6500], Intersection[IntegerDigits[ # ], {0, 1, 2, 3, 5, 7}] == {} & ] (* Ray Chandler, Mar 04 2007 *)
With[{c = {4, 6, 8, 9}}, Array[Select[Map[FromDigits@ Append[#, 9] &, Tuples[c, {#}]], PrimeQ] &, 4]] // Flatten (* Michael De Vlieger, Feb 02 2019 *)

Extended by Ray Chandler, Mar 04 2007

A152426 Primes that have both prime digits (2,3,5,7) and nonprime digits (0,1,4,6,8,9).

Original entry on oeis.org

13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 193, 197, 211, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 331, 347, 349, 359, 367, 379

Offset: 1

Omar E. Pol, Dec 03 2008

See also A152427, a subsequence without zeros.

Cf. A019546, A034844, A087363, A092621, A092626, A152312, A152313, A152427.

okQ[n_] := Module[{d=Union[IntegerDigits[n]]}, Length[Intersection[d, {2,3,5,7}]]>0 && Length[Intersection[d, {0,1,4,6,8,9}]]>0]; Select[Prime[Range[100]], okQ] (* T. D. Noe, Jan 20 2011 *)

Edited by Omar E. Pol, Jul 04 2009, Jan 20 2011

Definition clarified by N. J. A. Sloane, Jul 05 2009

A152427 Primes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9).

Original entry on oeis.org

13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 193, 197, 211, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 311, 313, 317, 331, 347, 349, 359, 367, 379, 383, 389, 397, 421, 431, 433, 439

Offset: 1

Omar E. Pol, Dec 03 2008

A000040 \ A034844 \ A019546.

Cf. A018252.

Cf. A018252, A019546, A034844, A087363, A092621, A092626, A152312, A152313, A152426.

okQ[n_] := Module[{d = Union[IntegerDigits[n]]}, Length[Intersection[d, {2, 3, 5, 7}]] > 0 && Length[Intersection[d, {1, 4, 6, 8, 9}]] > 0]; Select[Prime[Range[100]], okQ] (* T. D. Noe, Jan 21 2011 *)
pdQ[n_]:=Module[{idn=Select[IntegerDigits[n],#!=0&]},Count[idn,?PrimeQ]>0&&Count[idn,?(!PrimeQ[#]&)]>0]; Select[Prime[Range[100]],pdQ] (* Harvey P. Dale, Jan 31 2013 *)

a(n) ~ n log n

Corrected and extended by Harvey P. Dale, Jan 31 2013

A220488 Primes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9), without digits "0".

Original entry on oeis.org

13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 193, 197, 211, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 311, 313, 317, 331, 347, 349, 359, 367, 379, 383, 389, 397, 421, 431, 433, 439

Offset: 1

Omar E. Pol, Feb 01 2013

For similar sequences see A152426 and A152427.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A018252, A019546, A034844, A038618, A087363, A092621, A092626, A152312, A152313, A152426, A152427.

pdnpdQ[n_]:=Module[{idn=IntegerDigits[n],p,z=DigitCount[n,10,0]},p=Count[ idn,?PrimeQ];p>0&&z==0&&Length[idn]>p]; Select[ Prime[ Range[ 150]], pdnpdQ] (* _Harvey P. Dale, Oct 01 2013 *)

A215927 Primes having at least one digit that is not prime.

Original entry on oeis.org

11, 13, 17, 19, 29, 31, 41, 43, 47, 59, 61, 67, 71, 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, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 331, 347

Offset: 1

Luca Brigada Villa, Aug 27 2012

Complement of A019546 within the primes A000040.

			19 is in the sequence because neither of its two digits is prime, 1 being a unit and 9 being the square of 3.
23 is not in the sequence because both 2 and 3 are prime.
29 is in the sequence because 9 is not prime (though 2 is).

Cf. A000040, A019546, A034844, A033274, A152313, A141409.

[p: p in PrimesUpTo(500) | not Set(Intseq(p)) subset [2,3,5,7]]; // Vincenzo Librandi Oct 25 2016

Select[Prime[Range[100]], Complement[IntegerDigits[#], {2, 3, 5, 7}] != {} &] (* Alonso del Arte, Aug 27 2012 *)

is_A215927(n)=isprime(n)&apply(x->!isprime(x),eval(Vec(Str(n)))) \\ - M. F. Hasler, Aug 27 2012

a(55) corrected by Vincenzo Librandi, Oct 25 2016

A323391 Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.

Original entry on oeis.org

19, 41, 61, 89, 149, 419, 461, 491, 619, 641, 691, 941, 1489, 4691, 4861, 6481, 6491, 6841, 8419, 8461, 8641, 8941, 9461, 14869, 46819, 48619, 49681, 64189, 64891, 68491, 69481, 81649, 84691, 84961, 86491, 98641

Offset: 1

Bernard Schott, Jan 13 2019

There are only 36 terms in this sequence, which is a finite subsequence of A152313.
Two particular examples:
6481 is also the smallest prime formed from the concatenation of two consecutive squares.
81649 is the only prime containing all the nonprime positive digits such that every string of two consecutive digits is a square.

			14869 is the smallest prime that contains all the nonprime positive digits; 98641 is the largest one.

Chris K. Caldwell and G. L. Honaker, Jr., 81649, Prime Curios!

Subsequence of A152313. Subsequence of A029743. Subsequence of A155024 (with distinct nonprime digits but with 0) and of A034844.

Cf. A029743 (with distinct digits), A124674 (with distinct prime digits), A155045 (with distinct odd digits), A323387 (with distinct square digits), A323578 (with distinct digits for which parity of digits alternates).

Select[Union@ Flatten@ Map[FromDigits /@ Permutations@ # &, Rest@ Subsets@ {1, 4, 6, 8, 9}], PrimeQ] (* Michael De Vlieger, Jan 19 2019 *)

isok(p) = isprime(p) && (d=digits(p)) && vecmin(d) && (#Set(d) == #d) && (#select(x->isprime(x), d) == 0); \\ Michel Marcus, Jan 14 2019

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A034844 Primes with only nonprime decimal digits.

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A051416 Primes whose digits are composite; primes having only {4, 6, 8, 9} as digits.

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A152426 Primes that have both prime digits (2,3,5,7) and nonprime digits (0,1,4,6,8,9).

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A152427 Primes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9).

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A220488 Primes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9), without digits "0".

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A215927 Primes having at least one digit that is not prime.

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A323391 Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.

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