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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