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A242518
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Primes p for which p^n - 2 is prime for n = 1, 3, 5 and 7.
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2
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201829, 2739721, 6108679, 7883329, 9260131, 9309721, 9917389, 14488249, 15386491, 15876481, 16685299, 16967191, 18145279, 20566969, 20869129, 21150991, 23194909, 25510189, 28406929, 34669909, 35039311, 36795169, 37912141, 39083521, 39805639
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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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p = 201829 (prime)
p - 2 = 201827 (prime)
p^3 - 2 = 8221493263045787 (prime)
p^5 - 2 = 334902077869420623790640147 (prime)
p^7 - 2 = 13642217803107967058507788317851080907 (prime)
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MATHEMATICA
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Select[Prime[Range[25*10^5]], AllTrue[#^{1, 3, 5, 7}-2, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 26 2015 *)
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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)
....n4=((n**7)-2)
....##.Check if n1, n2, n3 and n4 are also primes
....if sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True and sympy.ntheory.isprime(n4)== True:
........print(n, " , " , n1, " , ", n2, " , ", n3, " , ", n4)
....n=sympy.ntheory.nextprime(n)
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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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