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A158295
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Primes p such that p^3-p-+1 are twin primes.
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3
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2, 11, 31, 41, 239, 521, 2309, 4099, 4409, 4441, 4651, 5009, 5039, 5261, 6481, 6871, 7129, 8609, 9391, 10259, 12841, 13759, 14519, 14879, 14939, 15569, 16871, 18451, 20369, 22441, 24049, 25841, 28151, 28279, 29429, 30181, 30631, 32089, 32299, 36781
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OFFSET
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1,1
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COMMENTS
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Primes p such that p^3+p-+1 are twin primes, so far only one: 3. 3^3+3=30-+1 = primes.
Primes in the sequence A236524. Odd primes are congruent to either 1 mod 10 or 9 mod 10. - Derek Orr, Jan 27 2014
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LINKS
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EXAMPLE
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2^3-2=6-+1 = 5,7 primes, 11^3-11-+1 = 1319,1321 primes...
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MATHEMATICA
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lst={}; Do[p=Prime[n]; a=p^3-p; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, p]], {n, 8!}]; lst
Select[Prime[Range[3500]], And@@PrimeQ[#^3-#+{1, -1}]&] (* Harvey P. Dale, Jan 05 2013 *)
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PROG
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(Python)
import sympy
from sympy import isprime
{print(p) for p in range(10**5) if isprime(p) and isprime(p**3-p-1) and isprime(p**3-p+1)} # Derek Orr, Jan 27 2014
(PARI)
s=[]; forprime(p=2, 40000, if(isprime(p^3-p-1) && isprime(p^3-p+1), s=concat(s, p))); s /* Colin Barker, Jan 28 2014 */
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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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