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A153590
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Primes p such that p^2+3p+1 is also prime.
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1
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2, 3, 5, 7, 19, 23, 29, 37, 43, 47, 53, 59, 67, 113, 137, 139, 157, 163, 173, 179, 229, 239, 257, 263, 293, 313, 349, 353, 359, 373, 379, 419, 449, 467, 499, 503, 509, 547, 577, 587, 593, 617, 643, 647, 653, 719, 727, 797, 883, 929, 967, 983, 997, 1013, 1033, 1049
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes p such that (p*(p+1))+(p+(p+1)) is prime. Primes p such that sum of product and the sum of p and the nextNumber is prime. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 13 2010]
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EXAMPLE
| For p = 2, p^2+3p+1 = 11 is prime; for p = 67, p^2+3p+1 = 4691 is prime; for p = 419, p^2+3p+1 = 176819 is prime.
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MATHEMATICA
| f[n_]:=n*(n+1)+(n)+(n+1); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst..and/or..Select[Table[Prime[n], {n, 6!}], PrimeQ[ #^2+3*#+1]&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 13 2010]
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PROG
| (MAGMA) [ p: p in PrimesUpTo(1050) | IsPrime(p^2+3*p+1) ];
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CROSSREFS
| Cf. A014574, A174242, A174243, A174244 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 13 2010]
Sequence in context: A000519 A088732 A129693 * A025019 A140327 A163074
Adjacent sequences: A153587 A153588 A153589 * A153591 A153592 A153593
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KEYWORD
| nonn
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 29 2008
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EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 01 2009
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