#primes — Public Fediverse posts

A072502: Numbers that are run sums (trapezoidal, the difference between two triangular numbers) in exactly 3 ways
A072502 ➡️ https://oeis.org/A072502

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072502.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072502.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072502.html

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

My data have not been verified but my work is highly reproducible.
- Downloads (csv, img, dump) ➡️ https://decompwlj.com/
- Algorithms ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

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

A072437: Numbers with no prime factors of form 4*k+3
A072437 ➡️ https://oeis.org/A072437

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072437.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072437.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072437.html

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

A072225: Numbers k such that prime(k) + prime(k+1) + prime(k+2) is prime
A072225 ➡️ https://oeis.org/A072225

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072225.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072225.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072225.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #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 #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

A072202: Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicity
A072202 ➡️ https://oeis.org/A072202

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072202.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072202.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072202.html

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

A072140: The period length of the 'Reverse and Subtract' trajectory of n is greater than 1
A072140 ➡️ https://oeis.org/A072140

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072140.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072140.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072140.html

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

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

A072055: a(n) = 2*prime(n)+1
A072055 ➡️ https://oeis.org/A072055

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072055.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A072055.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072055.html

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

A071403: Which squarefree number is prime? a(n)-th squarefree number equals n-th prime
A071403 ➡️ https://oeis.org/A071403

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A071403.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A071403.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A071403.html

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

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 ➡️ https://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

A071395: Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers)
A071395 ➡️ https://oeis.org/A071395

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A071395.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A071395.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A071395.html

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

A071139: Numbers k such that the sum of distinct primes dividing k is divisible by the largest prime dividing k
A071139 ➡️ https://oeis.org/A071139

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A071139.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A071139.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A071139.html

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

Decomposition into weight × level + jump of prime numbers:
- a new classification of primes ➡️ https://decompwlj.com/primedecomp.php
- in 3D - threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Prime_numbers.html

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

A070932: Possible number of units in a finite (commutative or non-commutative) ring
A070932 ➡️ https://oeis.org/A070932

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A070932.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A070932.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A070932.html

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

A070865: Smallest prime such that the difference of successive terms is strictly increasing
A070865 ➡️ https://oeis.org/A070865

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A070865.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A070865.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A070865.html

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

150 sequences decomposed into weight × level + jump in one GIF (log(weight),log(level)):
1000 sequences decomposed on https://decompwlj.com

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

A070552: Semiprimes k such that k+1 is also a semiprime
A070552 ➡️ https://oeis.org/A070552

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A070552.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A070552.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A070552.html

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

This animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com

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

4: The palindromes in base 10 (A002113) ➡️ https://decompwlj.com/3DgraphGen/Palindromes.html

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

3: The triangular numbers (A000217) ➡️ https://decompwlj.com/3DgraphGen/Triangular_numbers.html

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

2: The prime numbers (A000040) ➡️ https://decompwlj.com/3DgraphGen/Prime_numbers.html

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

Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
🧵⬇️

1: The natural numbers (A000027) ➡️ https://decompwlj.com/3DgraphGen/Natural_numbers.html

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

A069686: Primes whose internal digits form a prime
A069686 ➡️ https://oeis.org/A069686

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A069686.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A069686.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A069686.html

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

A069346: Primes of the form n - Omega(n), where Omega(n) is the number of prime factors of n, A001222(n)
A069346 ➡️ https://oeis.org/A069346

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A069346.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A069346.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A069346.html

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

A069059: Numbers k such that k and sigma(k) are not relatively prime
A069059 ➡️ https://oeis.org/A069059

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A069059.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A069059.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A069059.html

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

A068781: Lesser of two consecutive numbers each divisible by a square
A068781 ➡️ https://oeis.org/A068781

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068781.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A068781.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068781.html

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

A068780: Composite numbers n such that n+1 is also composite
A068780 ➡️ https://oeis.org/A068780

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068780.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A068780.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068780.html

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

A068501: Values m such that the consecutive pair parameters(m,m+1) generate Pythagorean triples whose odd terms are both prime
A068501 ➡️ https://oeis.org/A068501

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068501.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A068501.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068501.html

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

A067947: Numbers k such that k divides 7^k - 1
A067947 ➡️ https://oeis.org/A067947

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067947.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067947.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067947.html

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

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

A067945: Numbers k that divide 3^k - 1
A067945 ➡️ https://oeis.org/A067945

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067945.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067945.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067945.html

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

A067889: Primes sandwiched between two numbers having same number of divisors
A067889 ➡️ https://oeis.org/A067889

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067889.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067889.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067889.html

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

A067259: Cubefree numbers which are not squarefree
A067259 ➡️ https://oeis.org/A067259

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A067259.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A067259.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A067259.html

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

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

GPT5.6 Sol: "If decompwlj became a standard mathematical lens"

The most important conceptual impact would be a change of question. Instead of asking only, “What is the next term?” or “How fast does the sequence grow?”, researchers could also ask:
How does the next additive jump expose—or hide—the multiplicative structure behind the present term?
That is a legitimate and surprisingly rich question.

https://decompwlj.com/GPT5.6Sol_decompwlj_counterfactual_impacts_report_2026-08-11.html

For privacy: https://web.archive.org/web/20260811121838/https://decompwlj.com/GPT5.6Sol_decompwlj_counterfactual_impacts_report_2026-08-11.html

#decompwlj #math #AI #OpenAI #ChatGPT #GPT #GPT56Sol #GPTSol #sequence #numbers #graph #PrimeNumbers #NumberTheory #arithmetic #threejs #FTA #classification #research #FundamentalTheoremOfArithmetic #TwinPrimes #twin #primes #conjecture #sieveOfEratosthenes #Eratosthenes #sieve

Someone asked me about sexy cousins. I'll admit, I was briefly hopeful. Turns out they meant primes with gap 6 and gap 4 respectively.

Disappointed, I did what anyone would do and stayed up computing distinct-prime partitions of primes.

Define m_d<(p) as the minimum k such that prime p is a sum of k pairwise distinct primes, each strictly less than p. Set m_d<(p) = ∞ if no such decomposition exists.

For every prime p ≤ 10^8 (verified directly, ~30 seconds on commodity hardware):

• m_d<(11) = ∞, uniquely. 11 simply refuses to be built from smaller primes. Provable by exhaustion: the 11 subsets of {2,3,5,7} of size ≥ 2
sum to {5,7,8,9,10,12,14,15,17}. 11 is not invited.

• m_d<(17) = 4, uniquely. 17 needed all four of its juniors (2+3+5+7) just to show up. Overachiever or socially awkward — you decide.

• m_d<(p) ∈ {2, 3} for every other prime in range. 5,761,448 tested. All well-adjusted.

I don't know if this object has a name. I don't know if this is trivially known, or trivially reducible to something known.

The repo has code, a writeup, verification prompts you can feed to any LLM to check the claims, and some other things I found along the way.

https://github.com/keeltremor/goldeen
https://doi.org/10.5281/zenodo.19542143

If any of this rings a bell please let me know!
🐉

#numbertheory #primes

#numbertheory #partitions #primes #sexyprimes

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

One day, one decomposition
A000028: Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000028.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000028.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000028.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #factorization #PrimeNumbers #binary #expansions #graph #threejs #webGL

One day, one decomposition
A276078: Numbers n in whose prime factorization no exponent of any prime(k) exceeds k

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A276078.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A276078.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A276078.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #factorization #exponent #primes #PrimeNumbers #graph #threejs #webGL

Riffs and Rotes • Happy New Year 2025
• https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \text{Then} ~ 2025
= 81 \cdot 25
= 3^4 5^2 \)

\( = {p_2}^4 {p_3}^2
= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]

The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.

Riff 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png

Rote 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

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

https://www.youtube.com/watch?v=EK32jo7i5LQ

#dirichlet #euler #primes #totient #patterns #spirals #mod #residue #class #polar #math #amazing #plot #3blue1brown