home.social

#numbertheory — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #numbertheory, aggregated by home.social.

  1. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  2. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  3. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  4. We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

    #decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

  5. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  6. My first, favorite and most important sequence, the weights of prime numbers: A117078
    We see prime numbers classified by level and by weight on the graph.

    A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists ➡️ oeis.org/A117078

    #decompwlj #math #mathematics #maths #sequence #OEIS #graph #3D #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

  7. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  8. From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨

    In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,

    aᵖ ≡ a (mod p).

    For example, when p = 5:
    2⁵ − 2 = 30, which is divisible by 5, and
    3⁵ − 3 = 240, which is also divisible by 5.

    Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”

    About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.

    #Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge

  9. MOSS Season 2 continues next week.

    🎙️ Benjamin Wesolowski (CNRS & ENS Lyon, France)

    Talk title: Random walks in number-theoretic cryptology

    🗓️ Thursday, 7 May 2026 • 🕓 4:00 PM CEST • Online

    Abstract: Cryptography met number theory in 1976, when Diffie and Hellman achieved what had long been considered impossible: a protocol for two people to exchange secret information on a public channel, even if they had never met before to establish some kind of password, a pre-shared key. Diffie and Hellman designed the protocol such that a spy attempting to find the secret would need to solve a presumably hard computational problem: the discrete logarithm problem in the multiplicative group of a finite field.

    Since then, number theory has consistently met the challenges of cryptography, offering a variety of difficult algorithmic problems and powerful tools for their analysis. In this talk, we will explore this “mathematical cryptology”, with a focus on euclidean lattices (designed to resist against quantum computers), the use of random walks, and how spectral methods in number theory apply to cryptology.

    ----------------------------------------------

    Scan the QR code in the image to join the mailing list and receive the online access link.

    #Mathematics #NumberTheory #Cryptography #Lattices #PostQuantum #MOSS #EMS

  10. 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 ef.msp.org/articles/uploads/an

    #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