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A158295 Primes p such that p^3-p-+1 are twin primes. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

2^3-2=6-+1 = 5,7 primes, 11^3-11-+1 = 1319,1321 primes...

MATHEMATICA

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 *)

PROG

(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 */

CROSSREFS

Cf. A120364, A088483, A236524, A236477, A126421.

Sequence in context: A190154 A187830 A115058 * A213898 A085041 A197642

Adjacent sequences:  A158292 A158293 A158294 * A158296 A158297 A158298

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 15 2009

STATUS

approved

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)