

A158295


Primes p such that p^3p+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
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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

2^32=6+1 = 5,7 primes, 11^311+1 = 1319,1321 primes...


MATHEMATICA

lst={}; Do[p=Prime[n]; a=p^3p; If[PrimeQ[a1]&&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**3p1) and isprime(p**3p+1)} # Derek Orr, Jan 27 2014
(PARI)
s=[]; forprime(p=2, 40000, if(isprime(p^3p1) && isprime(p^3p+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



