In 2003 We Discovered a New Way to Generate Primes

There is a Fibonacci-like recurrence that seems to generate primes! It was discovered in 2003, but at the time no one understood why it worked. A few years later, I plotted the primes in a way that reveals some hidden structure. This is a tale of logarithmic scale.

Followup video on this sequence:    • Why Does this Algorithm Generate Primes?  

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References:

Fernando Chamizo, Dulcinea Raboso, and Serafín Ruiz-Cabello, On Rowland's Sequence, The Electronic Journal of Combinatorics 18(2) (2011) P10 (10 pages).
https://doi.org/10.37236/2006

Benoit Cloitre, 10 conjectures in additive number theory (2011) (46 pages).
https://arxiv.org/abs/1101.4274

Eric Rowland, A natural prime-generating recurrence, Journal of Integer Sequences 11 (2008) 08.2.8 (13 pages).
https://cs.uwaterloo.ca/journals/JIS/...

Serafín Ruiz-Cabello, On the use of the least common multiple to build a prime-generating recurrence, International Journal of Number Theory 13 (2017) 819–833.
https://doi.org/10.1142/S179304211750...
Open access: https://arxiv.org/abs/1504.05041

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0:00 Recurrence
2:59 Doubling relations
4:03 Plotting locations of primes
6:24 Clusters of primes
9:49 Predicting primes in each cluster
15:22 Answers to burning questions
18:19 Changing the initial term
20:08 Cloitre's lcm recurrence

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Animated with Manim. https://www.manim.community
Thanks to Ken Emmer for supplying the microphone.

Web site: https://ericrowland.github.io
Twitter:   / ericrowland