Ex-News Junkie
Prime numbers
Sat Aug 5, 2017 1:17pm
2001:1970:5c22:6100:3de7:9d8d:8202:580

More thoughts on how the universe is easier to understand if it is represented using polar coordinates, where there is only one dimension of space, and therefore space can only be curved if it is a "spiral".

Considering that we live in a universe that appears to exhibit a plethora of mathematical relationships, I wondered if there are any patterns in prime numbers if they are plotted on a spiral. So I generated the first 32,000 prime numbers (the hard way, by "trial division") and imagined them as angles instead of linear coordinates. Plotting them on a spiral made them appear very random just as they would on a linear plot. But I thought about how our one-dimension of space might have started out as an angular dimension before the Big Bang. So I played with the parameters, loosening or tightening the spiral and I noticed some patterns start to emerge. In fact, when I collapsed a spiral into a unit circle I discovered that all 32,000 prime numbers occurred at the exact same locations. All 32,000 prime numbers were multiples of a set of "root angles":

1,(2,3,5),7,11,13,17,19,23,29,
31,37,41,43,47,49,53,59,
61,67,71,73,77,79,83,89,
91,97,101,103,107,109,113,119,
121,127,131,133,137,139,143,149,
151,157,161,163,167,169,173,179,
181,187,191,193,197,199,203,209,
211,217,221,223,227,229,233,239,
241,247,251,253,257,259,263,269,
271,277,281,283,287,289,293,299,
301,307,311,313,317,319,323,329,
331,337,341,343,347,349,353,359.

I bracketed the angles 2,3,5 because they only occur once (the rest occurred over 300 times each). When angles 2,3,5 are removed from the first row, the next row can be obtained by adding 30 degrees, and the next row, and so on. So, the set of radial lines on which all primes are found... also repeat themselves in 30 degree angle increments! The radial pattern of prime numbers can be seen by plotting them on an Archimedes Spiral. What type & parameters of spiral our universe is currently in, I couldn't guess.

The caveat is that the root angles are not all prime numbers, e.g. 49, and not all multiples of these root angles are prime numbers. But the reverse is true... ALL prime numbers are multiples of these root angles. Of course I'm not a mathematician and I can't "prove" it. Empirically however, based on the fairly even distribution of my 32,000 prime numbers among all these root angle radii, I estimate that there is less than a 1/300 chance that my hypothesis is incorrect.

The universe makes a lot more sense in polar coordinates. I'm thinking "theory of everything".

For now I've found a faster way to generate lists of prime numbers by not only filtering even numbers, but filtering out any number that is not a multiple of a root angle. I still have to use "trial division" to test each root angle multiple to see if it is truly a prime number. Maybe there are more patterns to be found yet.

Here is an image of gravity waves generated by two black holes orbiting closely. They look like Archimedes Spirals:



Here is an image of the spiral "Whirlpool" galaxy M51 about 30 million light years away. I wonder if anything interesting occurs at "root angles" in a galaxy:


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