class group is trivial, the following statement is true: A prime p or its inverse –p is of the form ± p = x2 - 6y2 for integers x and y if and only if However, this statement is false if we focus only on p and not -p (and is in fact even false for p = 2), because the narrow class group is nontrivial. The statement that classifies the positive p is the following: A prime p is of the form p = x2 - 6y2 for integers x and y if and only if p = 3 or (Whereas the first statement allows primes , the second only allows primes .) See also Class group Quadratic form References A. Fröhlich and M. J. Taylor, Algebraic Number Theory (p. 180), Cambridge University Press, 1991. Algebraic number theory