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A190527
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Primes of the form p^4 + p^3 + p^2 + p + 1, where p is prime.
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8
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31, 2801, 30941, 88741, 292561, 732541, 3500201, 28792661, 39449441, 48037081, 262209281, 1394714501, 2666986681, 3276517921, 4802611441, 5908670381, 12936304421, 16656709681, 19408913261, 24903325661, 37226181521, 43713558101, 52753304641, 64141071121, 96427561501, 100648118041
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OFFSET
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1,1
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COMMENTS
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These primes are generated by exactly A065509, cf. 2nd formula.
These numbers are repunit primes 11111_p, so they are Brazilian primes (A085104).
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 30941 = 11111_13 = 13^4 + 13^3 + 13^2 + 13^1 + 1 is prime.
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MATHEMATICA
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a190527[n_] := Select[Map[(Prime[#]^5-1)/(Prime[#]-1)&, Range[n]], PrimeQ]
Select[#^4 + #^3 + #^2 + # + 1 &/@Prime[Range[100]], PrimeQ] (* Vincenzo Librandi, May 06 2017 *)
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PROG
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(Magma)[p: p in PrimesUpTo(600) | IsPrime(p) where p is p^4 +p^3+p^2+p+1]; // Vincenzo Librandi, May 06 2017
(PARI)
[q|p<-primes(100), ispseudoprime(q=(p^5-1)\(p-1))]
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CROSSREFS
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Subsequence of A088548 (primes n^4 + ... + 1) and A085104 ("Brazilian" primes, of the form 1 + n + n^2 + ... + n^k).
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KEYWORD
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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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