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A253941
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Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.
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4
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184279409, 619338131, 913749803, 1057351301, 1507289869, 1600204213, 2845213937, 4725908767, 4760956439, 5374709801, 5518707641, 8724256757, 9044067313, 9387396269, 10992352517, 11937043567, 13493126359, 13593105793, 17891702891, 17897035213, 17954907767, 19690938161, 20227580927, 20922685813, 21313027583, 21717176851
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OFFSET
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1,1
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COMMENTS
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The sequence contains all terms up to 10^10. There are no terms as yet for which (p^12 + 5)/6 is also prime.
No terms < 10^11 with (p^12 + 5)/6 prime. - Chai Wah Wu, Jan 27 2015
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LINKS
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PROG
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(Python)
from gmpy2 import is_prime, t_divmod
for p in range(1, 10**6, 2):
....if is_prime(p):
........p2, x = p**2, 1
........for i in range(5):
............x *= p2
............q, r = t_divmod(x+5, 6)
............if r or not is_prime(q):
................break
........else:
(PARI) lista(nn) = forprime(p=5, nn, if(ispseudoprime((p^2 + 5)/6) && ispseudoprime((p^4 + 5)/6) && ispseudoprime((p^6 + 5)/6) && ispseudoprime((p^8 + 5)/6) && ispseudoprime((p^10 + 5)/6), print1(p, ", "))); \\ Jinyuan Wang, Mar 01 2020
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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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