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:
“No Government can be long secure without a formidable Opposition. It reduces their supporters to that tractable number which can be managed by the joint influences of fruition and hope. It offers vengeance to the discontented, and distinction to the ambitious; and employs the energies of aspiring spirits, who otherwise may prove traitors in a division or assassins in a debate.”
—Benjamin Disraeli (1804–1881)