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: https://youtu.be/2y_6IIXAI_s ---------------- 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/VOL11/Rowland/rowland21.html 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/S1793042117500439 Open access: https://arxiv.org/abs/1504.05041 ---------------- 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 ---------------- Animated with Manim. https://www.manim.community Thanks to Ken Emmer for supplying the microphone. Web site: https://ericrowland.github.io Twitter: https://twitter.com/ericrowland