A061371 Composite numbers with all prime digits.

22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77, 222, 225, 232, 235, 237, 252, 253, 255, 272, 273, 275, 322, 323, 325, 327, 332, 333, 335, 352, 355, 357, 372, 375, 377, 522, 525, 527, 532, 533, 535, 537, 552, 553, 555, 572, 573, 575, 722, 723, 725, 732, 735

Offset: 1

Author

Amarnath Murthy, May 02 2001

Keywords

• nonn
• base

Examples

			35 is composite with digits 3 and 5 which are primes.
22 is composite and has prime digits, twice 2;
573 is composite and has prime digits, 3, 5 and 7.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A061372.

Programs

Magma

[ n: n in [22..736] | not IsPrime(n) and Set(Intseq(n)) subset [2,3,5,7] ];  // Bruno Berselli, Dec 21 2011

Maple

stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end:
ts_stnepf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='false') then stpf:=stpf+1; # number of nonprime digits fi od; RETURN(stpf) end:
ts_nepr_neprn0:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( isprime(i)='false' and ts_stnepf(i) = 0) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_nepr_neprn0(4000); # Jani Melik, Apr 11 2004

Mathematica

With[{comps=Complement[Range[1000],Prime[Range[PrimePi[1000]]]]}, Select[ comps, And@@PrimeQ[IntegerDigits[#]]&]] (* Harvey P. Dale, Dec 21 2011 *)
Table[Select[FromDigits/@Tuples[{2,3,5,7},n],CompositeQ],{n,2,4}]//Flatten (* Harvey P. Dale, Oct 05 2019 *)

Python

from sympy import isprime
from itertools import count, islice, product
def agen(): yield from (t for d in count(2) for p in product("2357", repeat=d) if not isprime(t:=int("".join(p))))
print(list(islice(agen(), 54))) # Michael S. Branicky, Jun 30 2025

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 08 2001