a080076.json, sorted array of all 122,742 Proth primes less than 2^40 (> 10^12)
repo containing all Proth primes k*2^m+1 with odd 0<k<1200 and all 0<m<3,600,000
Phi3.gp: 72 Phi(3,x) primes from top 5000 known primes (t5k.org), and verification of fast determination of sqrt(-1) (mod p)
repo: 10:45:01h AMD 7600X computation of "sqrt(-1) (mod p)" (and sum of two squares) for 9,383,761-digit prime p
repo: sqrt(-1) (mod p) as well as sum of squares p=x^2+y^2 for 6 Colbert primes p
repo: About 6.7 day computation of "sqrt(-1) (mod p)" for 11,887,192-digit prime p, largest known prime =1 (mod 4) Later I learned how to determine sqrt(-1) (mod p) for that p=Phi(3,-516693^1048576) and sum of two squares in just 347ms in total … ;-)
repo: [x,y,s] for top 10 known primes p with s²=-1 (mod p) and p=x²+y² (all above 6million decimal digits)
RSA_numbers_factored.py provides access to RSA numbers (up to 2048-bit or 617-digit),
and their prime factors for those that have been factored sofar (up to RSA-250).
Provides access to prime factorization dictionaries for p-1 and q-1 for RSA-l=n=p*q as well
(up to RSA-220),
for efficient totient_2() and reduced_totient_2() functions.
Python script is transpiled manually to RSA_numbers_factored.js for use in browser and with nodejs;
using arbitrary precision arithmetic BigInt type (Python number type provides arbitrary precision arithmetic).
Github repo: https://github.com/Hermann-SW/RSA_numbers_factored
2D PostScript output as well:
(planar graphs are 4colorable, there is a linear time 5coloring algorithm, and even simpler linear time six_coloring(G))
Planar graph embedding onto sphere is not that easy. Just mapping plane embedding onto sphere and then using spring embedder might unravel (left) all vertices into same place (right):
Work in progress algorithm node.tetra.js OpenSCAD output:
JSCAD output:
The repo provides spherical edge, half vertex and vertex text, and spherical polygon modules/functions to generate sphere embedding OpenSCAD/JSCAD output.
Provides "vertex()" and "edge()" OpenSCAD modules for drawing graph onto cube[oid] as well, here visualization of "cube[oid] shortest surface path problem" solution, details: https://forums.raspberrypi.com/viewtopic.php?p=2038730#p2038730 (orange/blue/yellow shortest paths pass through 3/4/5 faces, from single bottom face start point to top face target point)
straight_line_graphviz.cpp takes a LEDA format undirected graph as input.
Then calls BGL (Boost Graph Library) "make_connected()", "make_biconnected_planar()", "make_maximal_planar()" and finally "chrobak_payne_straight_line_drawing()" to create the vertex coordinates of a planar staight line drawing. Makes use of pos="x,y!" feature that neato layout engine provides, and dot layout engine does not. So neato is not used as layout engine at all, but only to display the straight line drawing determined with this gist using GraphvizFiddle.
C/C++ scripts / (tcc) "-run" option for gcc and g++ (for Linux ELF, verified for x86_64 and armv7l)
ELF executable gets compiled into RAM, and executed from there — no auxiliary filesystem files!
<peg-solitaire/> (1-player board game [browser XSLT])
It knows all solutions for 33/37/39 pegs English/French/3-3-2-2 boards.
You may choose "Cheat" link (based on 1+16+64=81GB data files on this website).
There are 2,990,375,067 good positions for French board that allow to end with single peg on target field (forum link).
Instructions on how to revert a move can be found just above that posting (animation):
new binomial formula "C(a+b,c) = sum(k=0..a, …" and animation in A007318
Blue links in .svg work; "10-edge CCs" at bottom right uses GraphvizFiddle mentioned above for display.
Before that, submitted 4 interlaced bisections found manually.
Raspberry camera / gstreamer / raspivid / raspiraw
Teaser video of a closing mouse trap; the whole closing is completed in 0.01s(!).
This is an animation from Raspberry v2 camera 640x75 video captured at 1007fps(!), played at 1fps.
When the mouse trap bar touches down, it hits the black piezo igniter, showing a spark in front (this is frame 1281)
Multiple exposures of 84.3m/s (303km/h) inflight airgun bullet (1012x760 frame scaled to 25%, github repo)
… slightly faster than 5m/s (18km/h) raspcatbot target speed.
Just to get an idea of what autonomous line following at maximal speed will have to deal with.
1kg raspcatbot running (with steel wire rope) on 1.25m radius around screw in garage floor.
Speed 3.24m/s or 11.65km/h, kinetic energy 0.5*m*v² = 5.25 Joule, centripetal force m*v²/r = 8.4 kg*m/s²
youtube video of unplanned backward roll high in the air
full stop back wheelies
• U-turn w/o speed (>2m/s) reduction
• just swap one motor's direction for some time
• slowed down by factor 90/25=3.6
• 90fps slowmo youtube video
• positions at start of (overshooted) U-turn, at 90°, 180° and finally before going straight again
• Arduebot can do similar U-turn
For fun I registered as participant of South-German (Bavaria, Baden-Württemberg, Hesse and Saxony) 100km road race championship 1998 in Leipzig. There were 59 starters, 52 finishers, and I was 50th finisher (at age of 33). There were only 6 starters in male 30-34 age group, and only 3 of them were from South-Germany. One South-German starter did not finish -- therefore I got official silver medal from German Athletics Association(!), was "2nd best South-German 100km road race runner in age group 30-34 in 1998" … ;-)
[winner finished in 7:07h, I finished in 12:26h -- better than 8km/h on average]