

A359414


Primes prime(k) such that prime(k)^2 + prime(k+1)^2  1 is the square of a prime.


0




OFFSET

1,1


COMMENTS

There are no more terms < 10^100 unless the prime gap g = prime(k+1)  prime(k) exceeds 10000. For all known terms, g <= 14. There are no more terms < 10^1000 with g <= 14.  Jon E. Schoenfield, Dec 31 2022


LINKS



EXAMPLE

a(3) = 23 is a term because 23 is prime, the next prime is 29, and 23^2 + 29^2  1 = 37^2 where 37 is prime.


MAPLE

R:= NULL: q:= 2:
while q < 2*10^8 do
p:= q; q:= nextprime(q);
r:= p^2 + q^2  1;
if issqr(r) and isprime(sqrt(r)) then R:= R, p fi
od:
R;


CROSSREFS



KEYWORD

nonn,more,less


AUTHOR



STATUS

approved



