[By the way, nifty use of the blackboard font ℚ!] I didn't know the discover of the irrationality of sqrt(2) was known by name! I'd like to see a reference for that, since I always heard the history was unclear. ----- The Heegner numbers are 1, 2, 3, 7, 11, 19, 43, 67, 163. The ℚ(√−1) numbers are known as Gaussian integers. The ℚ(√−3) numbers are known as Eisenstein integers. The ℚ(√−7) numbers are known as Kleinian integers. It's bugged me for awhile that ℚ(√−2) wasn't named. Today I decided that the obvious name was ... The ℚ(√−2) numbers are now known as Hippasus integers. Hippasus proved √2 was irrational. He was then murdered. Seemed like an apt name to use. I calculated the nine types of Heegner primes and plotted them out. http://community.wolfram.com/groups/-/m/t/965609 <http://community.wolfram.com/groups/-/m/t/965609> Anyone agree / disagree about calling ℚ(√−2) the Hippasus integers? ----- I might be misinterpreting what is meant by "The ℚ(√[whatever]) numbers" are known as [whoever] integers." Usually ℚ(√[whatever]) is labeled an example of a "number field", which I think is any field of algebraic numbers with a finite index over ℚ. But to use the word "integers" implies that they are the roots of monic polynomials, with integer coefficients, that lie in the number field. For the number field ℚ(√-h) where h is a Heegner number the set of algebraic integers is as follows: Let O_h be the ring of algebraic integers of ℚ(√-h), Then: O_1 = Z[i] O_2 = Z[sqrt(-2)] O_h = Z[(1 + sqrt(h))/2] for h = -3, -7, -11, -19, -43, -67, -163. —Dan