Eric Rowland | In 2003 We Discovered a New Way to Generate Primes @EricRowland | Uploaded 1 year ago | Updated 3 hours ago
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: youtu.be/2y_6IIXAI_s
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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).
doi.org/10.37236/2006
Benoit Cloitre, 10 conjectures in additive number theory (2011) (46 pages).
arxiv.org/abs/1101.4274
Eric Rowland, A natural prime-generating recurrence, Journal of Integer Sequences 11 (2008) 08.2.8 (13 pages).
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.
doi.org/10.1142/S1793042117500439
Open access: 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
----------------
Animated with Manim. https://www.manim.community
Thanks to Ken Emmer for supplying the microphone.
Web site: ericrowland.github.io
Twitter: twitter.com/ericrowland
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: 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).
doi.org/10.37236/2006
Benoit Cloitre, 10 conjectures in additive number theory (2011) (46 pages).
arxiv.org/abs/1101.4274
Eric Rowland, A natural prime-generating recurrence, Journal of Integer Sequences 11 (2008) 08.2.8 (13 pages).
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.
doi.org/10.1142/S1793042117500439
Open access: 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: ericrowland.github.io
Twitter: twitter.com/ericrowland
