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A046703
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Multiplicative primes: product of digits is a prime.
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10
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2, 3, 5, 7, 13, 17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 113111, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 1171111, 11111117, 11111131, 11111171, 11111311, 11113111, 11131111
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OFFSET
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1,1
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COMMENTS
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Primes with one prime digit and all other digits are 1. The linked table includes probable primes. -Jens Kruse Andersen,Jul 21 2014
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LINKS
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MATHEMATICA
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Select[Prime[Range[740000]], PrimeQ[Times@@IntegerDigits[#]]&] (*Harvey P. Dale,Oct 02 2011 *)
Select[FromDigits/@Flatten[Table[Permutations[PadRight[{p}, n, 1]], {n, 8}, {p, {2, 3, 5, 7}}], 2], PrimeQ]//Union (*Harvey P. Dale,Nov 21 2019 *)
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PROG
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(PARI) f(n, b, d) = if(d, f(10*n+1, b, d-1); if(!b, forprime(q=2, 9, f(10*n+q, 1, d-1))), if(b && isprime(n), print1(n "," )))
select( is_A046703(n)=isprime(vecprod(digits(n)))&&ispseudoprime(n), [0..9999]) \\ This defines is_A046703(). In older PARI versions, vecprod=factorback.
next_A046703(n)={if( n>1, until( ispseudoprime(n), my(d=digits(n)); n=fromdigits( apply( t->if(t>1, nextprime(t+1), 1), d))+(d[1]>5)); n, 2)}
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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