login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Prime p such that p^5 + p^3 + p - 4 is prime.
2

%I #9 Jul 03 2016 00:14:42

%S 3,5,11,19,23,37,43,103,127,193,199,239,269,277,283,373,397,457,467,

%T 509,751,761,887,919,947,977,1019,1039,1051,1069,1087,1277,1307,1481,

%U 1531,1549,1559,1613,1759,2003,2017,2243,2311,2357,2417,2447,2467,2473,2671,2851,2963,3089,3253,3257,3323,3433,3463,3511,3539

%N Prime p such that p^5 + p^3 + p - 4 is prime.

%H Abhiram R Devesh, <a href="/A243899/b243899.txt">Table of n, a(n) for n = 1..10000</a>

%e Prime p = 3 is in this sequence as p^5 + p^3 + p - 4 = 269 (prime).

%e Prime p = 5 is in this sequence as p^5 + p^3 + p - 4 = 3251 (prime).

%t Select[Prime[Range[500]], PrimeQ[#^5+#^3+#-4]&] (* _Harvey P. Dale_, Jul 03 2015 *)

%o (Python)

%o import sympy.ntheory as snt

%o p=1

%o while p>0:

%o ....p=snt.nextprime(p)

%o ....pp=p+(p**3)+(p**5)-4

%o ....if snt.isprime(pp) == True:

%o ........print(p, pp)

%K nonn,easy

%O 1,1

%A _Abhiram R Devesh_, Jun 14 2014