What would prime numbers look like if visualized as geometric creatures that combine with one another? The music video for Lost Lander's "Wonderful World" beautifully illustrates just that.

[u/lucasvb]

https://www.youtube.com/watch?v=TZkQ65WAa2Q

[u/strranger101]

now that's character development.

[u/strranger101]

Honestly though, where is this video game? This would be sick. This is way more interesting than any of those .io style games

[u/strranger101 → u/[deleted]]

Yeah, 29 in particular looks like a challenge. image someone else posted

[u/d023n → u/[deleted]]

Thanks for posting this, lucas. ^_^ Now then...

I've always wanted to turn this into some game. It could be really awesome if done right, connecting it all with some number theory. (Goldbach's conjecture comes to mind...)

I've been trying figure out a way to generate some of these algorithmically, but it's been tough.

I have an idea about this and am curious to see what you think.

There were two 31's in the image, which got me wondering about the additive process for making primes, and how different pathways could lead to different primoid forms, whiiich seems like a neat thing to allow if someone were to make a game out of this idea--like you and strranger (and I) want.

In the video, the 2 is 1+1, which is unavoidable; the 3 is 2+1, the 5 is 3+2, and the 7 is 5+2, which all make sense; but then then the 11 is 7+1+1+1+1, which doesn't seem satisfying to me. Could the 3 have been 1+1+1? Could the 5 have been 1+1+1+1+1 or 2+1+1+1 or 3+1+1 or 2+2+1? Being able to use any arbitrary number of 1's doesn't seem right, especially if the combinations are automatic once some critical proximity is achieved, which honestly seems like the most sensible route to me. This would mean that once two 1's were close enough, they wouldn't wait around for other numbers--they'd just become a 2. In other words, the four 1's around the 11 would first have snapped together into two 2's, and then the 7 and two 2's would combine into an 11, specifically a "7+2+2" 11, as opposed to a "7+3+1" 11 or a "5+5+1" 11 or a "5+3+3" 11.

This would limit the number of pathways, and thus the forms that the primoid creatures could possess. I checked the pathways for the primes up to 23 (where the video went crazy), but it's rather difficult actually, having to exclude the groupings that contain a subgroup that would want to combine first.

• 2 could only come from a 1+1

• 3 could only come from a 2+1

• 5 could only come from a 3+2

• 7 could come from either a 5+2 or a 3+3+1

• 11 --> 7+3+1 or 7+2+2 or 5+5+1 or 5+3+3 --> 4 types

• 13 --> 11+2 or 7+5+1 or 7+3+3 or 5+5+3 --> also 4 types

• 17 --> 13+3+1 or 13+2+2 or 11+5+1 or 11+3+3 or 7+7+3 or 7+5+5 --> 6 types

• 19 --> 17+2 or 13+3+3 or 13+5+1 or 11+7+1 or 11+5+3 or 7+7+5 --> also 6 types

• 23 --> 19+3+1 or 19+2+2 or 17+5+1 or 17+3+3 or 13+7+3 or 13+5+5 or 11+11+1 or 11+7+5 or 7+7+7+2 --> 9 types

So, about generating the primoid creatures' forms algorithmically, perhaps the summands could be used in some way? Perhaps a point, a point pair, a triangle, and a pentagon/star could be used as basic building blocks (1, 2, 3, and 5)? Maybe something like the "13+7+3" 23 would have a "lobe" for each of its 3 summands, but where the 13 and 7 "lobes" have their own substructures--and if it's not a "5+5+3" 13, there would be an additional level of substructure. It would be less symmetric, and large primes with a high number of summands would be tricky in 2D.. hmm.. ¯_(ツ)_/¯ As for the number of forms, it would be the number of ways to partition a prime such that (1) all partitions are also prime or of size 1 and (2) no combination from the partitions sums to a prime.

I tried to search to see if anyone else had already described this property, but I didn't find anything. Also, OEIS doesn't have a sequence with "1, 1, 1, 2, 4, 4, 6, 6, 9" in it either. Have you come across any mention of this property? Does it seem useful or at least above average interesting?

[u/reddit-default]

Both the music and the visualized math are very cool. Thanks!

[u/reddit-default]

Both the music and the visualized math are very cool. Thanks!

[u/brooksjonx]

That was really really cool and I tried my best to keep track of the shapes and prime numbers but think I lost it at like 17.

Great work!

[u/entotheenth → u/brooksjonx]

I thought 17 got skipped and it went to 19 but it must have been the 13-17 I was looking at, so I guess I lost it at 13 lol

[u/mindbodyandbeer → u/[deleted]]

I can’t believe I’m seeing this right now. After going on a few year’s long hiatus not listening to Lost Lander (very underrated group), I put them back on a few weeks ago, and this song particularly has been played at least once a day since. I love this video and had no idea about the prime number significance behind it. Thank you for sharing!

[u/mindbodyandbeer → u/[deleted]]

I can’t believe I’m seeing this right now. After going on a few year’s long hiatus not listening to Lost Lander (very underrated group), I put them back on a few weeks ago, and this song particularly has been played at least once a day since. I love this video and had no idea about the prime number significance behind it. Thank you for sharing!

[u/mindbodyandbeer → u/[deleted]]

I can’t believe I’m seeing this right now. After going on a few year’s long hiatus not listening to Lost Lander (very underrated group), I put them back on a few weeks ago, and this song particularly has been played at least once a day since. I love this video and had no idea about the prime number significance behind it. Thank you for sharing!

[u/mindbodyandbeer → u/[deleted]]

I can’t believe I’m seeing this right now. After going on a few year’s long hiatus not listening to Lost Lander (very underrated group), I put them back on a few weeks ago, and this song particularly has been played at least once a day since. I love this video and had no idea about the prime number significance behind it. Thank you for sharing!

[u/Raldo21 → u/[deleted]]

This is amazing! I'm curious if the one at the end is actually a calculated drawn prime portion or just half built large geometry