In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #numbers #TwinPrimes #conjecture #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #numbers #TwinPrimes #twin #primes #conjecture #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
3/3
Quadratic primes as they relate to #twinprimes and pairs of twin primes
The prime number 233 at the intersection of these two diagonal runs of prime numbers isn’t a twin prime but as an inevitable consequence of the way diagonals work, it’s immediately below the twin primes 197 and 199 and above the twin primes 269 and 271. Above and below that are cousin primes and above and below that are sexy primes.
In isolation I think that would be great but an intersection number like 233 isn’t particularly rare. At a slightly wider view, you can see really clearly where these diagonal runs intersect and in almost every case you’ll find either twin primes or, in a lot of cases, a pair of twin primes above and below the intersection.
One avenue for further research (that’s far above my skill level) is to prove if these runs of quadratic primes are infinite. If they always exist, then the diagonal runs of primes will intersect and wherever they do, you’ll definitely find twin primes, cousin primes, sexy primes. In lots of cases each will come in pairs.
Sidebar about Euler’s prime generating function
If you look to the right of the column of consecutive square numbers there are some amazing examples of quadratic progressions of primes. Notably there’s a diagonal run of primes matching Euler’s prime generating function k2 − k + 41 which has 40 or so consecutive primes.
I'd love to hear anyone's feedback on this. Particularly without a proper name for the quadratic progressions, it makes it impossible for me to google and see what else has been written about them. Happy to discuss or explain things better. Thanks for getting this far.
#Primes in quadratic progression 1/3
I’ve been looking at primes in what I’m calling quadratic progression but I don’t really know if that name is accurate or if there’s already a name for them. I’ve found some patterns that relate to #twinprimes and I’ve also made a video of this idea if that’s more your jam. http://www.youtube.com/watch?v=DiTRYaja4pY
I’ve created a sieve where the width of the table changes on each row. It’s right-justified so consecutive square numbers line up down the right hand side. Effectively each row has all the positive whole numbers smaller than the square number to the left. It’s triangular. I’ve created a triangle.
When you highlight all the prime numbers there are some obvious patterns for composites. All the even numbers form a grid. If you count the right column with the squares as column zero and count from the right, all the columns corresponding to square number are entirely composite except for the top number in some cases (like the right column in the sieve of Eratosthenes).
There’s no clear pattern to the primes. All the primes are on diagonals because every other diagonal is odd but there’s nothing un-interrupted where you’d confidently predict where the primes were.
Linear progressions
I see other amateur mathematicians trying to find primes by starting at say 7 and adding 6 repeatedly which results in a bunch of prime numbers - 13, 19, 25 is not a prime but 31, 37, 43 are. And while that linear approach is interesting, it’s not much more complicated than saying that primes don’t have 2 or 3 as factors. I think the prime progressions in this sort of visualisation are far more interesting. They follow the same sort of pattern but the number you add increases by 2 each step.
I made a series of six videos for SOME1 about #primenumbers and where to find them. In total it runs to about 35 minutes.
https://www.youtube.com/playlist?list=PLhMQ5JG0CnKmfTIpKLAVspEfqhnjRoRVH
The short version is that I've used the difference of two squares to test for primality, set bounds for those squares and then sieve the squares using modularity to infinitely optimise the primality test. I also look at primes in quadratic progression and how that relates to twin primes and Euler's prime generating function and some other stuff.
I'm pretty interested in feedback on my ideas around primes which, from my perspective, are entirely original and true but may bewell established and I just haven't seen it because I can't read maths papers. I'm not great at maths but I'm pretty good with google and I'm yet to find anything close to what I've done.
Please reach out if you watch it and get anything out of it.
#primes #factorisation #twinprimes #quadraticprogression #numbertheory #sieve #SieveOfEratosthenes
A review of V1 of the paper "On the Infinitude of Twin Primes" by Dr. Ryan Matthew Thurman ( @rythur ).
Shared in one of his posts under the url https://ef.msp.org/articles/uploads/ant/submitted/230524-Thurman/230524-Thurman-v1.pdf
#TwinPrimes #Primes #NumberTheory
#TwinPrimeConjecture #UnsolvedProblem #Proof #SolvedProblem
#Simple #Insightful #PrimeClockMethod #Modulo
#Puzzle #GameLike #Thrilled #Captivating #Excitement #Reading #ReadingRecommendation
My background for this review: a layman person without any #degree, with very weak #Math interest (I knew what were prime numbers but never heard of the twin prime conjecture) and lack of math background except for what is taught in high school and the occasional math that pop here and there from my adjacent interests in the process of thinking of process both formal and informally (mainly from #lisp lore for the #ComputerScience side and #Hegel lore for the #Philosophy side of the story)
And now, only after almost 1 month since I have read it, will I review this paper (flushed face 😳).
A paper of 10 pages of content.
The paper is very pleasant and simple to read. Managing to catch our attention and make us read it in one sitting with a child-like excitement and joy. So if you have tendencies to leave things half-done, do not fear, you will get drawn into finishing it without having to fight a moment of boringness.
1/3
Hello! It occurs to me I haven't actually made an #introduction / #introductions / #interests post yet, so now is as good a time as any.
My name is WhenGryphonsFly! I'm a computer programmer with an interest in #ElectoralReform, such as #ProportionalRepresentation, #STARVoting, and #UncapTheHouse. I am also interested in #CopyrightReform, such as reduction of term lengths (20 years or less), expansion of fair use (particularly in regards to derivative works), and expansion of compulsory licensing (for everything, basically). Some of my other interests include #FuckCars, #FourDayWorkWeek and #SixHourWorkDay, #Corvid (especially #BlueJay), #ProgrammingLanguage design (I'm making my own!), #GameBoyAdvance, #Pokemon, and #TwinPrimes.
I mostly lurk and boost, as my social anxiety unfortunately extends to social media. Still, I'm glad to be here!
* Note: while my stance on copyright in general might imply I support Copilot, Stable Diffusion, etc.; I emphatically do not.
(Edit: I adjusted the formatting, then realized I liked it better the old way)
Rémi Eismann
ƧƿѦςɛ♏ѦਹѤʞ
Ben
IrrenWirr
WhenGryphonsFly "
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Pustam | पुस्तम | পুস্তম🇳🇵