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A091305
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Primes of the form p*q - p - q, where p and q are primes.
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3
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3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 59, 71, 79, 83, 101, 103, 107, 131, 137, 139, 149, 163, 167, 179, 191, 197, 199, 211, 223, 227, 239, 251, 263, 269, 271, 281, 311, 331, 347, 359, 379, 383, 419, 431, 443, 461, 463, 467, 479, 491, 499, 503, 521, 523
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OFFSET
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1,1
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COMMENTS
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Some primes have no unique representation (besides of symmetry in p,q!), e.g. 11 with (p,q)=(2,13) and (3,7).
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LINKS
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EXAMPLE
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31 is a member with p=3, q=17.
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MATHEMATICA
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mp[{p_, q_}]:=p*q-p-q; Take[Union[Select[mp/@Subsets[Prime[Range[100]], {2}], PrimeQ]], 60] (* Harvey P. Dale, Nov 27 2011 *)
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PROG
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(PARI) isA091305(p)=fordiv(p++, d, if(isprime(d+1)&isprime(p/d+1), return(isprime(p-1)))) \\ Charles R Greathouse IV, Feb 15 2011
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CROSSREFS
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Primes of the form p*q + p + q: A066938. Primes of the form p*q + p - q: A091301.
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KEYWORD
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easy,nice,nonn
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AUTHOR
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STATUS
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approved
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