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A157677
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Primes p such that p + (product of digits of p) is also prime.
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7
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23, 29, 61, 67, 83, 101, 103, 107, 109, 163, 233, 239, 283, 293, 307, 347, 349, 401, 409, 431, 439, 443, 449, 499, 503, 509, 563, 569, 601, 607, 613, 617, 619, 653, 659, 677, 683, 701, 709, 743, 809, 907, 929, 941, 1009, 1013, 1019, 1021, 1031, 1033, 1039
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OFFSET
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1,1
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COMMENTS
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If p contains a zero, then p is trivially a member.
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LINKS
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FORMULA
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EXAMPLE
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83 is prime, and 83 + 8*3 = 89 which is also prime. 103 is prime, and 103 + 1*0*3 = 103 is also prime. Thus 89 and 103 are members.
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MAPLE
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a := proc (n) local nn: nn := convert(ithprime(n), base, 10): if isprime(ithprime(n)+product(nn[j], j = 1 .. nops(nn))) = true then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 180); # Emeric Deutsch, Mar 08 2009
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MATHEMATICA
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Select[Prime[Range[175]], PrimeQ[# + Times @@ IntegerDigits[#]] &] (* Jayanta Basu, Apr 22 2013 *)
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PROG
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(PARI) dprod(n)=n=digits(n); prod(i=1, #n, n[i])
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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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