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A243817
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Primes p for which p - 4 and p^3 - 4 are primes.
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3
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11, 17, 23, 41, 83, 101, 131, 227, 311, 383, 491, 503, 773, 827, 881, 887, 971, 1097, 1283, 1301, 1451, 1493, 1877, 2141, 2243, 2273, 2351, 2687, 2861, 2957, 3533, 3881, 3947, 4007, 4517, 4643, 5231, 5237, 5573, 5741, 6203, 7211, 7541, 7883, 7937, 8741, 9137, 9551, 10337, 11447
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OFFSET
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1,1
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COMMENTS
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This is a subsequence of A046132: Larger member p+4 of cousin primes (p, p+4).
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LINKS
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EXAMPLE
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p = 11 is in this sequence because p - 4 = 7 (prime) and p^3 - 4 = 1327 (prime).
p = 17 is in this sequence because p - 4 = 13 (prime) and p^3 - 4 = 4909 (prime).
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PROG
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(Python)
import sympy.ntheory as snt
n=5
while n>1:
....n1=n-4
....n2=((n**3)-4)
....##Check if n1 and n2 are also primes.
....if snt.isprime(n1)== True and snt.isprime(n2)== True:
........print(n, n1, n2)
....n=snt.nextprime(n)
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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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