0

$$ \frac{log(4750778730825177725463920948909726618214491718039471366318747406368792)}{ sqrt(652) } - \tau = -2.54282421310320265217436545223140117387 E-78 $$ found with Pari GP by playing with $e^{\tau \sqrt{163*4}}$ where $\pi := \frac{\tau}{2}$. See https://en.wikipedia.org/wiki/Almost_integer#Almost_integers_relating_to_e_and_%CF%80

Is this known?

anomaly
  • 25,364
  • 5
  • 44
  • 85
John Nicholson
  • 446
  • 3
    https://en.wikipedia.org/wiki/Heegner_number – Count Iblis Mar 25 '19 at 04:20
  • 1
    Kindly consider improving the title of your question. Cheers :) – Paras Khosla Mar 25 '19 at 05:21
  • 1
    @johnnicholson It's clear you're devoted to $\tau$ but your current rep ($314$) betrays you. I think you need to double it, and fast. :) – Deepak Mar 25 '19 at 06:10
  • 2
    $e^{\pi\sqrt{163}}$ is close to an integer, so $e^{\tau\sqrt{163\cdot 4}} = (e^{\pi\sqrt{163}})^4$ will of course also be close to an integer. – eyeballfrog Mar 25 '19 at 06:11
  • @eyeballfrog Thanks. that does explain it a bit. My mind was not in gear, but do go on with an answer as to why this is true. With the sign change in the error as I subtracted of pi instead of tau and came out closer value too. – John Nicholson Mar 25 '19 at 10:50

0 Answers0