MathLapse - Meditation on Primes

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MathLapse - Meditation on Primes

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Christian Gaier

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The number line is winded up to an Archimedean spiral, which is known as Sacks number spiral, …

… in contrast to Ulam’s prime spiral, where the number line is winded up to a rectangular spiral. The distance between the numbers is slowly decreased leading to a circular motion in clockwise direction. A smooth color range from purple for digit 0 at the unit position of the integers to yellow for digit 9 is used. The black lines, which are later on shortened to dots, mark primes. As it can be seen, primes are usually chaotically distributed. However, at special times of the video 1:03, 2:07, 4:15 and 8:29, primes are forming very interesting patterns. At these times, the distance between integers is 2*pi-, pi-, pi/2- and pi/4-times the distance of the spiral arms. Just look and be amazed about the mysteries of mathematics!

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