163 and Ramanujan Constant

e^{\pi \sqrt{163}}
is almost a whole number !

\sqrt{-163}
is the last one of the list d which allows unique prime factorization in Z[d].

d =  \sqrt{-1}, \sqrt{-2}, \sqrt{-3}, \sqrt{-7}, \sqrt{-11}, \sqrt{-19}, \sqrt{-43}, \sqrt{-67}, \sqrt{-163}

Why \sqrt{-5} not in d?

6 = 2 x 3
6 = (1 + \sqrt{-5}).(1 - \sqrt{-5})

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One thought on “163 and Ramanujan Constant

  1. Pingback: Our Daily Story #9: The Indian Clerk Mathematician | Math Online Tom Circle

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