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A160858
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Primes p such that p^3-p^2-1 and p^3-p^2+1 are prime
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2
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2, 3, 13, 541, 859, 1279, 1459, 1951, 2239, 2971, 3181, 4003, 4129, 6343, 7393, 8053, 9043, 9463, 10501, 10831, 12433, 14083, 14731, 15073, 15991, 16603, 17443, 17491, 17761, 18493, 19861, 20173, 20323, 20929, 21391, 22963, 23071
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OFFSET
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1,1
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LINKS
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EXAMPLE
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3^3-3^2=27-9=18-+1=primes
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MATHEMATICA
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lst={}; Do[p=Prime[n]; a=p^2; b=p^3; c=b-a; If[PrimeQ[c-1]&&PrimeQ[c+1], AppendTo[lst, p]], {n, 2*7!}]; lst
Select[Prime[Range[3000]], AllTrue[#^3-#^2+{1, -1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 20 2018 *)
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PROG
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(PARI) forprime(p=2, 1e6, if(isprime(p^3-p^2-1)&&isprime(p^3-p^2+1), print1(p", ")))
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CROSSREFS
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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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