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A243583
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Primes p for which p + 4 and p^3 + 4 are primes.
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5
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3, 7, 19, 79, 103, 109, 277, 379, 487, 967, 1489, 1663, 1867, 2857, 3019, 3253, 3613, 3697, 4003, 4783, 4969, 5413, 5437, 5503, 5569, 5647, 5923, 7477, 7669, 7687, 7699, 7789, 7933, 8233, 8779, 9007, 9319, 9547, 9739, 10597, 11257, 11467, 11593, 11827, 12037
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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:
A023200: Primes p such that p + 4 is also prime.
A073573: Numbers n such that n^3 + 4 is prime.
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LINKS
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EXAMPLE
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p = 3 is in this sequence because p + 4 = 7 (prime) and p^3 + 4 = 31 (prime).
p = 7 is in this sequence because p + 4 = 11 (prime) and p^3 + 4 = 347 (prime).
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PROG
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(Python)
import sympy.ntheory as snt
n=2
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)
(PARI) s=[]; forprime(p=2, 20000, if(isprime(p+4) && isprime(p^3+4), s=concat(s, p))); s \\ Colin Barker, Jun 11 2014
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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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