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Heegner number
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==Class 2 numbers== The three numbers 88, 148, 232, for which the imaginary [[quadratic field]] <math>\Q\left[\sqrt{-d}\right]</math> has [[ideal class group|class number]] 2, are not Heegner numbers but have certain similar properties in terms of [[almost integer]]s. For instance,<ref>{{Cite web|author=Titus Piezas|url=https://www.oocities.org/titus_piezas/Ramanujan_a.pdf|title=Ramanujan’s Constant e^(pv163) And Its Cousins}}</ref> <math display=block>\begin{align} e^{\pi \sqrt{88}} +8\,744 &\approx \phantom{00\,00}2\,508\,952^2-0.077\dots\\ e^{\pi \sqrt{148}} +8\,744 &\approx \phantom{00\,}199\,148\,648^2-0.000\,97\dots\\ e^{\pi \sqrt{232}} +8\,744 &\approx 24\,591\,257\,752^2-0.000\,0078\dots\\ \end{align} </math> and <math display=block>\begin{align} e^{\pi \sqrt{22}} -24 &\approx \phantom{00}\left(6+4\sqrt{2}\right)^{6} +0.000\,11\dots\\ e^{\pi \sqrt{37}} +24 &\approx \left(12+ 2 \sqrt{37}\right)^6 -0.000\,0014\dots\\ e^{\pi \sqrt{58}} -24 &\approx \left(27 + 5 \sqrt{29}\right)^6 -0.000\,000\,0011\dots\\ \end{align} </math>
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