

A122710


Primes of the form p^2 + q^8 where p and q are primes.


1



281, 617, 1097, 1217, 5297, 10457, 17417, 19577, 23057, 32297, 39857, 44777, 52697, 58337, 72617, 167537, 192977, 212777, 241337, 249257, 383417, 398417, 502937, 517217, 564257, 704177, 830177, 885737, 943097, 982337, 1018337, 1038617, 1079777, 1442657, 1515617, 1560257, 1692857, 1745297, 1985537
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OFFSET

1,1


COMMENTS

p and q cannot both be odd. Thus p=2 or q=2. There are no primes of the form 2^2 + q^8 (consider divisibility by 5). Hence all solutions are of the form p^2 + 2^8 and are congruent to 7 mod 10.


LINKS



FORMULA



EXAMPLE

a(1) = 5^2 + 2^8 = 281.
a(2) = 19^2 + 2^8 = 617.
a(3) = 29^2 + 2^8 = 1097.


MAPLE

N:= 10^6: # to get terms up to N
select(isprime, [seq(2^8 + p^2, p = select(isprime, [5, seq(seq(10*i+j, j=[1, 9]), i=1..isqrt(N2^8)/10)]))]); # Robert Israel, Jan 24 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



