Breaking the #Factorization #Barrier : Medium

This state’s #Power #Prices are #Plummeting as it nears 100% #Renewables : New Sci

Why ‘activating’ your vagus nerve has become the latest wellness trend : Misc

Latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

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

Performance and Numerical Aspects of Decompositional Factorizations with FP64 Floating-Point Emulation in INT8

#NVIDIA #Int8 #FP64 #Factorization

https://hgpu.org/?p=30278

More #quantum computer #factorization fun:

https://www.johndcook.com/blog/2025/09/28/extrapolating-quantum-factoring/

If we extrapolate from the two points we have, factoring '15' in 2001 and '21' (kind of) in 2012, and would like to be able to factorize a 1024 bit number in 2035, we should be able to factorize 40 bit numbers now. Which we don't.

The author proposes to add new data points as they come in. I'm looking forward to that :)

This is excellent:

Replication of Quantum Factorisation Records with an 8-bit Home Computer, an Abacus, and a Dog

https://eprint.iacr.org/2025/1237.pdf

Selected hilarious quotations:

We use the UK form “factorise” here in place of the US variants “factorize” or “factor” in order to avoid the 40% tariff on the US term.

Similarly, we refer to an abacus as “an abacus” rather than a digital computer, despite the fact that it relies on digital manipulation to effect its computations.

The VIC-20 was a popular home computer in the 1980s that used the then popular 6502 microprocessor from 1975. Since this processor uses transistors, and transistors work by using quantum effects, a 6502 is as much a quantum device as is a D-Wave “quantum computer”

#vic20 #quantumComputing #factorization #factorisation

Harnessing Batched BLAS/LAPACK Kernels on GPUs for Parallel Solutions of Block Tridiagonal Systems

#ROCm #CUDA #BLAS #Factorization #Package

https://hgpu.org/?p=30168

LOL

"In this paper we showed how to replicate current quantum factorisation records using first a VIC-20 8-bit home computer from 1981, then an abacus, and finally a dog....[W]e rank a VIC-20 above an abacus, an abacus above a dog, and a dog above a quantum factorisation physics experiment. Finally, we provided standard evaluation criteria for future claimed quantum factorisations."

#physics #vic20 #factorization #quantumbullshit #quantumcomputing #funny #dogs #abacus

https://eprint.iacr.org/2025/1237.pdf

> Researchers claim to have used a #quantumComputer to factor a 2,048-bit #RSA integer.

> But the RSA number evaluated was the product of two prime factors that were too close together.

> As with a parlor magician's card deck that's been stacked for a card trick

> #Quantum #factorization is performed using sleight-of-hand numbers that have been selected to make them very easy to factorize using a #physics experiment

https://www.theregister.com/2025/07/17/quantum_cryptanalysis_criticism/

#quantumComputing #computerScience #cryptography

Researchers Use 1981 Home Computer to Match #Quantum #Factorization Records, Exposing Limitations

https://biggo.com/news/202507131329_Home_Computer_Matches_Quantum_Factorization_Records