Answers suggest hat you basically pick a random large odd number, and add 2 to it until your selected primality test passes.
The prime number theorem tells us that the probability that a number between 1 and is a prime number is .
Therefore, for an N-bit integer, we only have to run the test N times on average to find a prime.
Since say, A 512-bit integer is already humongous and sufficiently large, we would only need to search 512 times on average even for such sizes, and therefore the procedure scales well.
RSA vs Diffie-Hellman by Ciro Santilli 40 Updated 2025-07-16
As its name indicates, Diffie-Hellman key exchange is a key exchange algorithm. TODO verify: this means that in order to transmit a message, both parties must first send data to one another to reach a shared secret key. For RSA on the other hand, you can just take the public key of the other party and send encrypted data to them, the receiver does not need to send you any data at any point.
Basically the same content as: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), but maybe there is some merit to this talk, as it is a bit more direct in some points. This is consistent with what is mentioned at www.feynman.com/science/qed-lectures-in-new-zealand/ that the Auckland lecture was the first attempt.
By Mill Valley, CA based producer "Sound Photosynthesis", some info on their website: sound.photosynthesis.com/Richard_Feynman.html
They are mostly a New Age production company it seems, which highlights Feynman's absolute cult status. E.g. on the last video, he's not wearing shoes, like a proper guru.
Feynman liked to meet all kinds of weird people, and at some point he got interested in the New Age Esalen Institute. Surely You're Joking, Mr. Feynman this kind of experience a bit, there was nude bathing on a pool that oversaw the sea, and a guy offered to give a massage to the he nude girl and the accepted.
youtu.be/rZvgGekvHest=5105 actually talks about spin, notably that the endpoint events also have a spin, and that the transition rules take spin into account by rotating thing, and that the transition rules take spin into account by rotating things.
Next.js by Ciro Santilli 40 Updated 2025-07-16
Framework built on top of React.
Officially recommended by React[ref]:
Recommended Toolchains
If you’re building a server-rendered website with Node.js, try Next.js.
Basically what this does is to get server-side rendering just working by React, including hydration, which is a good thing.
Next.js sends the first pre-rendered HTML page along with the JavaScript code. Then, JavaScript page switches just load the API data.
Next.js does this nicely by forcing you to provide page data in a serialized JSON format, even when rendering server-side (e.g. the return value of getServerSideProps). This way, it is also able to provide either the full HTML, or just the JSON.
Some general downsides:
  • it does feel like they don't document deployment very well however, especially non-Vercel options, which is the company behind Next.js. I'm unable to find how to use a non Vercel CDN with ISR supposing that is possible.
  • Next.js is very opinionated, and like any opinionated library it is sometimes hard to know why something is/isn't happening, and sometimes it is hard/impossible to do what you want with it unless they add support. They have done good progress, but even as of 2022, some aspects just feel so immature, some major-looking use cases are not very well done.
In theory, Next.js could be the "ultimate frontend framework". It does have a lot of development difficulties that need to be ironed out, but the general concepts, and things it tries to integrate, including e.g. webpack, TypeScript, etc. are good. Maybe the question is when will someone put it together with an amazing backend library and dominate and finally put an end to the infinite number of Js Frameworks!
In order to offer its amazing features, Next.js is also extremely opinionated, which means that if something wasn't designed to be possible, it basically isn't.
No prerender with custom server? It forces you to write your API with next as well? Or does it mean something else?
TODO can it statically generate pages that are created at runtime? E.g. if I create a new blog post, will it automatically upload a static page? It seems that yes, and that this is exactly what Incremental Static Regeneration means:However, Ciro can't find any mention of how to specify where the pages are uploaded to... this is pat of the non-Vercel deployment problem.
Can't ISR prerenter by URL query parameters:That plus the requirement to have one page per file under pages/ leads to a lot of useless duplication, because then you are forced to place the URL parameters on the pathnames.
"Module not found: Can't resolve 'fs'" Hell. The main reason this happens seems to be the that in a higher order component, webpack can't determine if callbacks use the require or not to remove it from frontend code. Fully investigated and solved at:
Determines energy. This comes out directly from the resolution of the Schrödinger equation solution for the hydrogen atom where we have to set some arbitrary values of energy by separation of variables just like we have to set some arbitrary numbers when solving partial differential equations with the Fourier series. We then just happen to see that only certain integer values are possible to satisfy the equations.
The direction however is not specified by this number.
To determine the quantum angular momentum, we need the magnetic quantum number, which then selects which orbital exactly we are talking about.
Fixed quantum angular momentum in a given direction.
Can range between .
E.g. consider gallium which is 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1:
The z component of the quantum angular momentum is simply:
so e.g. again for gallium:
Note that this direction is arbitrary, since for a fixed azimuthal quantum number (and therefore fixed total angular momentum), we can only know one direction for sure. is normally used by convention.
This is a bit "formal hocus pocus first, action later". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.
Lecture notes transcribed by a student: github.com/avstjohn/qft
18 1h30 lectures.
NumPy by Ciro Santilli 40 Updated 2025-07-16
The people who work on this will go straight to heaven, no questions asked.
Scikit-learn by Ciro Santilli 40 Updated 2025-07-16
Examples under python/sklearn
. .venv/bin/activate
pip install sklearn matplotlib seaborn

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact