primes q = 3 mod 4 below 10^6: 39322 (note: 39,322)
Lemma 5.1 and Theorem 1.3 (tree sum of W_4 = 5q^2 with coprime positive rational arms) for all 39322 primes: a^2+ab+b^2 form 19668, 3Y^2-X^2 form 19654, failures 0 []
Theorem 1.4 on 3000 random parameter sets (d, A, B, k): failures 0
Theorem 1.4 examples 9(4c^2+1), c >= 2, 3 does not divide c: [153, 585, 909, 1773, 2313, 3609]
Proposition 7.1: 300 random nonseparable multigraphs with prime tau, 1190 vertex pairs u != v: q | tau(H/uv) in 0 cases
Corollary 7.2: 45: positive representations a^2+b^2 = [(3, 6), (6, 3)]; 1+c^2 = 5 prime: True
Corollary 7.2: 245: positive representations a^2+b^2 = [(7, 14), (14, 7)]; 1+c^2 = 5 prime: True
Corollary 7.2: 2313: positive representations a^2+b^2 = [(3, 48), (48, 3)]; 1+c^2 = 257 prime: True
