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A242517
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List of primes p for which p^n - 2 is prime for n = 1, 3, and 5.
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3
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31, 619, 2791, 4801, 15331, 33829, 40129, 63421, 69151, 98731, 127291, 142789, 143569, 149971, 151849, 176599, 184969, 201829, 210601, 225289, 231841, 243589, 250951, 271279, 273271, 277549, 280591, 392269, 405439, 441799, 472711, 510709, 530599, 568441, 578689
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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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31 is in the sequence because
p = 31 (prime),
p - 2 = 29 (prime),
p^3 - 2 = 29789 (prime), and
p^5 - 2 = 28629149 (prime).
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MATHEMATICA
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Select[Range[600000], PrimeQ[#] && AllTrue[#^{1, 3, 5} - 2, PrimeQ] &] (* Amiram Eldar, Apr 06 2020 *)
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PROG
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(Python)
import sympy
n=2
while n>1:
....n1=n-2
....n2=((n**3)-2)
....n3=((n**5)-2)
....##Check if n1, n2 and n3 are also primes.
....if sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True:
........print(n, " , " , n1, " , ", n2, " , ", n3)
....n=sympy.ntheory.nextprime(n)
(PARI) isok(p) = isprime(p) && isprime(p-2) && isprime(p^3-2) && isprime(p^5-2); \\ Michel Marcus, Apr 06 2020
(PARI) list(lim)=my(v=List(), p=29); forprime(q=31, lim, if(q-p==2 && isprime(q^3-2) && isprime(q^5-2), listput(v, q)); p=q); Vec(v) \\ Charles R Greathouse IV, Apr 06 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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