--- In

primenumbers@yahoogroups.com, James Merickel <moralforce120@...> wrote:

>

> I think that having gone through (at least) 5 editions and been scrutinized by all of the best number theorists in the world for the better part of a century makes this a safe assumption.

> JGMÂ

>

Chapter 15 of Hardy/Wright looks to me like the basis

for the issquare functions. Can the appropriate issquare

for A = 14x^2 + 14xy + y^2 be expressed as 7(2x + y)^2 = 2A?

To get back to the original conjectures, I don't see how

it immediately follows from Hardy/Wright Theorem 257 that

A = 5x^2 + 5xy + y^2 has as values ALL of the possible

values of primes that are +/- 1 mod 10 while the similar

B = 5x^2 + 25xy + y^2 will not.

I also don't see how it immediately follows that

A = 2x^2 + 2xy + y^2 has as values ALL of the

possible values of primes that are +1 mod 4

while the similar B = 8x^2 + 8xy + y^2 will not.

Surely there must be more to the proofs than just

reading the definitions found in chapter 15.

Aldrich