A321890 Primes of the form p^2 + 16 where p is prime.

41, 137, 857, 977, 1697, 6257, 7937, 11897, 22817, 32057, 36497, 44537, 52457, 78977, 96737, 151337, 160817, 177257, 192737, 249017, 326057, 361217, 434297, 477497, 491417, 516977, 546137, 564017, 591377, 674057, 737897, 776177, 885497, 942857, 982097, 1018097

Offset: 1

Author

Pierandrea Formusa, Nov 20 2018

Keywords

• nonn
• easy

Comments

Also primes of the form p^2 + q^4 where p and q are primes. The proof of the equivalence of the set of primes p^2 + q^4, where p and q are primes, with respect to this sequence, is the following: Exactly 1 of (p, q) giving a term is 2. q^4 + 4 is divisible by 5 and/or composite and gives no terms. - David A. Corneth, Nov 21 2018

Examples

			41 is prime and 41 = 5^2 + 16, where 5 is prime, therefore 41 is a term.
		

Programs

Maple

select(isprime,[ithprime(p)^2+16$p=1..180]); # Muniru A Asiru, Nov 24 2018

Mathematica

Select[Prime[Range[100]]^2+16, PrimeQ] (* Amiram Eldar, Nov 21 2018 *)

MiniZinc

include "globals.mzn";
int: n = 1;
int: max_val = 1200000;
array[1..n+1] of var 2..max_val: x;
% primes between 2..max_valset of int:
prime = 2..max_val diff { i | i in 2..max_val, j in 2..ceil(sqrt(i)) where i mod j = 0} ;
set of int: primes;primes = prime union {2};
solve satisfy;
constraint all_different(x) /\ x[1] in primes /\ x[2] in primes /\
pow(x[1],2)+16= x[2] ;
output [ show(x)]

PARI

upto(n) = my(res = List()); forprime(p = 3, sqrtint(n-16), if(isprime(p^2 + 16), listput(res, p^2 + 16))); res \\ David A. Corneth, Nov 21 2018

Extensions

More terms from Amiram Eldar, Nov 21 2018