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A065509
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Primes p such that p^4 + p^3 + p^2 + p + 1 is prime.
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7
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2, 7, 13, 17, 23, 29, 43, 73, 79, 83, 127, 193, 227, 239, 263, 277, 337, 359, 373, 397, 439, 457, 479, 503, 557, 563, 617, 919, 967, 1009, 1129, 1187, 1249, 1297, 1327, 1429, 1493, 1553, 1579, 1657, 1663, 1979, 1987, 2069, 2243, 2383, 2617, 2663, 2789
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(4) = 17 because 17 is prime and 17^4 + 17^3 + 17^2 + 17 + 1 = 88741 is prime.
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MATHEMATICA
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Select[Prime[Range[500]], PrimeQ[Total[#^Range[0, 4]]]&] (* Harvey P. Dale, Apr 08 2017 *)
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PROG
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(PARI) { n=0; for (m=1, 10^9, p=prime(m); if (isprime(p^4 + p^3 + p^2 + p + 1), write("b065509.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 20 2009
(PARI) {A065509_vec(N, p=1)=vector(N, i, until(isprime((p^5-1)\(p-1)), p=nextprime(p+1)); p)} \\ M. F. Hasler, Mar 03 2020
(Magma) [n: n in [0..10000]| IsPrime(n) and IsPrime(n^4+n^3+n^2+n+1)] // Vincenzo Librandi, Aug 07 2010
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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