Prime visualisations – or what is the 67 meme
The article discusses a new visualization technique for prime numbers using 3D cubes. It highlights the significance of the number 67 in this context, as it represents the smallest cube dimension that can be completely filled with numbers when viewed from certain angles. The author, a recreational mathematician, emphasizes that while the underlying mathematics is established, the visualization tool offers a fresh perspective on prime gaps.
- ▪The visualization of prime numbers in 3D cubes reveals interesting patterns and gaps.
- ▪The number 67 is identified as the smallest cube dimension that can be fully filled when viewed from specific angles.
- ▪The author created the visualization tool using Copilot and GPT-5.4, aiming to enhance understanding of prime numbers.
Opening excerpt (first ~120 words) tap to expand
primestuff I was looking at Visualization of Prime Numbers and had a thought. If you graph the primes in 3d cubes like: [ [ # PRIMES [1,2,3], # 2, 3 [4,5,6], # 5 [7,8,9] # 7 ], [ [10,11,12], # 11 [13,14,15], # 13 [16,17,18] # 17 ], [ [19,20,21], # 19 [22,23,24], # 23 [25,26,27] # - ] ] Projected onto a 2D surface and considering only the primes, this looks like. # Front [ [19,2,3], [13,5,-], [7,17,-] ] # Side [ [2,11,19], [5,13,23], [7,17,-] ] # Top [ [7,2,3], [13,11,-], [19,23,-] ] # The series of primes in the side view are: 2, 5, 7, 11, 13, 17, 19, 23 If the series is new, I will come up with a name. The longest line of primes in any direction within this graph is length 3 - [3, 5, 7]. Here's some visualisations.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at GitHub.