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A127882
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Primes of the form 60*(x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1).
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6
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163, 977611, 12294697, 37985853397, 49252877161, 137434331779, 830329719061, 1626105882361, 8060524420261, 11467771684597, 13008402510163, 15315610041211, 43633838254429, 71635442712061, 125119099806661
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OFFSET
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1,1
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COMMENTS
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Generating polynomial is Schur's polynomial of 5-degree. Schur's polynomials n degree are n-th first term of series expansion of e^x function. All polynomials are non-reducible and belonging to the An alternating Galois transitive group if n is divisible by 4 or to Sn symmetric Galois Group in other case (proof Schur, 1930).
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LINKS
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MAPLE
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select(isprime, [seq(60*(x^5/120+x^4/24+x^3/6+x^2/2+x+1), x=1..2000)]); # Muniru A Asiru, Apr 30 2018
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MATHEMATICA
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a = {}; Do[If[PrimeQ[60 + 60*x + 30*x^2 + 10*x^3 + (5*x^4)/2 + x^5/2], AppendTo[a, 60 + 60*x + 30*x^2 + 10*x^3 + (5*x^4)/2 + x^5/2]], {x, 1, 1000}]; a
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PROG
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(GAP) Filtered(List([1..2000], x->60*(x^5/120+x^4/24+x^3/6+x^2/2+x+1)), IsPrime); # Muniru A Asiru, Apr 30 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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