Lipschitz primes

Here we see Lipschitz primes (a,b,c,d) on the 3D hyper plane a=701.
Lipschitz Primes

Hurwitz primes

Here we see Hurwitz primes (a,b,c,d) + (1,1,1,1)/2 on the 3D hyper plane a=3001, where the density is a bit lower already.
Hurwitz Primes