In number theory, a Heegner number is a square-free positive integer d such that the imaginary quadratic field Q(√−d) has class number 1. Equivalently, its ring of integers has unique factorization.
The determination of such numbers is a special case of the class number problem, and they underlie several striking results in number theory.
According to the Stark–Heegner theorem there are precisely nine Heegner numbers:
- 1, 2, 3, 7, 11, 19, 43, 67, 163.
This result was conjectured by Gauss and proven by Kurt Heegner in 1952.
Read more about Heegner Number: Euler's Prime-generating Polynomial, Almost Integers and Ramanujan's Constant, Other Heegner Numbers, Consecutive Primes
Famous quotes containing the word number:
“I have known a number of Don Juans who were good studs and who cavorted between the sheets without a psychiatrist to guide them. But most of the busy love-makers I knew were looking for masculinity rather than practicing it. They were fellows of dubious lust.”
—Ben Hecht (1893–1964)