|
|
A193051
|
|
Primes p such that 12*p^2-1 and 16*p^3-1 are also primes.
|
|
1
|
|
|
2, 3, 17, 29, 107, 167, 173, 599, 1667, 1889, 2129, 3407, 3539, 3797, 3863, 5189, 6779, 6983, 7529, 8849, 11399, 11519, 11657, 12227, 12437, 12809, 13217, 14153, 15227, 16223, 16607, 17609, 21683, 21863, 22193, 23789, 25127
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Primes p such that 3*(2p)^2-1 (see A089681) and 2*(2p)^3-1 are primes.
|
|
LINKS
|
|
|
EXAMPLE
|
For p=2, 2 is a prime number, 12*2^2-1=47 is a prime number and 16*2^3-1=127 is a prime number.
For p=3, 3 is a prime number, 12*3^2-1=109 is a prime number and 16*3^3-1=431 is a prime number.
|
|
MATHEMATICA
|
fQ[n_] := PrimeQ[12 n^2 - 1] && PrimeQ[16 n^3 - 1]; Select[ Prime@ Range@ 3000, fQ] (* Robert G. Wilson v, Aug 08 2011 *)
Select[Prime[Range[5000]], PrimeQ[12 #^2 - 1] && PrimeQ[16 #^3 - 1]&] (* Vincenzo Librandi, Apr 10 2013 *)
|
|
PROG
|
(Magma) [p: p in PrimesUpTo(26000)|IsPrime(12*p^2-1) and IsPrime(16*p^3-1)]; // Vincenzo Librandi, Apr 10 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|