Saw this statement on another site: "Any prime number higher than three, when squared and subtracted by one, will always turn out to be a multiple of 24."
I never heard of this one before. Is there a proof of this property? Definitely needs a bit more investigation.
Spectacular Connection Between #LLMs, #QuantumSystems, and #NumberTheory
DataScienceCentral.com https://www.datasciencecentral.com/spectacular-connection-between-llms-quantum-systems-and-number-theory/
M. Prime Newtons gives a better inductive proof than that Geordie shark does. (-:
I'm not ready enough to send it to a real preprint server, but here is the current version of my Prouhet-Thue-Morse paper. It contains:
https://github.com/LivInTheLookingGlass/Thue-Morse/blob/main/rendered.pdf
@mattmcirvin @graveolensa #math #mathematics #maths #ThueMorse #ProuhetThueMorse #NumberTheory
TIL: Fermi-Dirac-Primes.
(Not primes, but you can multiply them to get any integer. Construcing a number this way, any f-d-prime will occur at most once as factor. This has been compared to fermion behavior, and hence the name.)
https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_prime
2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, ...
#math #NumberTheory
A #geometry masterpiece: #Yale prof solves part of math’s #RosettaStone.
Yale’s #SamRaskin has solved a major portion of a math question that could lead to a translation #theory for some areas of #math.
❛❛ The [Robert] #Langlands Conjectures … suggested in the 1960s that deep, unproven connections exist between #numbertheory, harmonic analysis & #geometry — 3 areas of math long considered distinctly separate. ❜❜
https://news.yale.edu/2024/11/01/geometry-masterpiece-yale-prof-solves-part-maths-rosetta-stone 01 Nov 2024 https://Wikipedia.org/wiki/Langlands_program
Overdue #introduction post:
• US Midwest
• Married with cats
• Liberal af
• This is not my only Mastodon account, but it is the one with my name and face on it.
• I've worked 30 years in software, but I've stepped away from it to go to grad school for #math at Indiana State University.
• Even before grad school, I was studying #NumberTheory and other topics for fun.
• Need a #tutor? DM me to ask about math, physics, and stats tutoring at the college level. (Motivated high school students also considered!)
• I studied #physics for undergrad & still watch the frontiers of the field.
@Kencf618033
Infinitely many one would assume(?)
#maths #math #numbertheory
A curious math problem I came up with: given a target, what's the fewest digits an integer must have (in a given base) to contain all integers from 0 to the target, as substrings?
http://wok.oblomov.eu/mathesis/number-substrings/
@mathematics @math@lemmy.ml @math@kbin.social
e.g. for a target of 19 a candidate representative would be 1011213141516171819 in base 10, that has 19 digits. Can it be done in less, or is $\sigma_10(19) = 19$?
Can we find a general rule? Any properties of this function?
A short story about my decomposition into weight × level + jump. It's a new fundamental theorem of arithmetic and academia is 11 years late.
When Thomas Oliver and Kyu-Hwan Lee used machine learning techniques to predict the ranks of elliptic curves with high accuracy, they noticed hidden oscillations reminiscent of bird murmurations. That pattern was not noticed by mathematicians before, and an explicit formula for those was found by Nina Zubrilina.
https://www.quantamagazine.org/elliptic-curve-murmurations-found-with-ai-take-flight-20240305/
#EllipticCurves #NumberTheory #Cryptography #ECC
@mcnees @Mikebrown Eris discovered on the 5th day of the 5th year of the millennium in data from 10/21 (10/2 × 1 = 5 (!)) of 2003 (2+0+0+3=5 (!)): the Law of Fives is more and more manifest the harder you look (and never wrong!)
#decompwlj 
It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. For natural numbers, the weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1).
For prime numbers, this decomposition led to a new classification of primes. Primes classified by weight follow Legendre conjecture and i conjecture that primes classified by level rarefy. I think this conjecture is very important for the distribution of primes.
It's easy to see and prove that lesser of twin primes (>3) have a weight of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a weight of 3.
I am not mathematician so i decompose sequences to promote my vision of numbers. By doing these decompositions, i apply a kind of sieve on each sequences.
https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump
Big news in the world of math because I know that you care. 
"Mathematicians Discover The Ninth Dedekind Number, After 32 Years of Searching
Undeterred after three decades of looking, and with some assistance from a supercomputer, mathematicians have finally discovered a new example of a special integer called a Dedekind number.
Only the ninth of its kind, or D(9), it is calculated to equal 286 386 577 668 298 411 128 469 151 667 598 498 812 366, if you're updating your own records. This 42 digit monster follows the 23-digit D(8) discovered in 1991."
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
Dreamer, wanderer, mathematician in England's inland West
Je m’excuse de faire des pouets pour le moment en anglais surtout, cependant il faut que je vous prévienne que je regarde et lis und Toots auf Deutsch sehe ich oder so
#NumberTheory #maths #HigherEducation
#PoetryLovers #BookLovers #bookstodon #bookshelf #hauntology #scifi
#art #museums #ModernArt #ContemporaryArt #pottery #ceramic #GenerativeArt #MastoArt #hiking
Hello #mathstodon, it’s great to be here! Hard to #introduce myself in 500 chars but here we go:
I currently work as an #SRE where I enjoy automating my job. I’ve also studied electron #optics at one of the world’s largest #laser facilities, built robotic tools for the #Apple #FaceID team, and written firmware for #autonomouscar #radar sensors.
I’m passionate about #combinatorics , #gametheory , and #numbertheory.
In my spare moments you can find me #composing #music, #hiking, and #reading.
Just trying some tags to see what pops up.
#AbstractAlgebra
#bioinformatics
#numbertheory
#EmbarcaderoDelphi
#cplusplus
ѦਹѤʞ 
