Results for
I am thrilled python interoperability now seems to work for me with my APPLE M1 MacBookPro and MATLAB V2025a. The available instructions are still, shall we say, cryptic. Here is a summary of my interaction with GPT 4o to get this to work.
===========================================================
MATLAB R2025a + Python (Astropy) Integration on Apple Silicon (M1/M2/M3 Macs)
===========================================================
Author: D. Carlsmith, documented with ChatGPT
Last updated: July 2025
This guide provides full instructions, gotchas, and workarounds to run Python 3.10 with MATLAB R2025a (Apple Silicon/macOS) using native ARM64 Python and calling modules like Astropy, Numpy, etc. from within MATLAB.
===========================================================
Overview
===========================================================
- MATLAB R2025a on Apple Silicon (M1/M2/M3) runs as "maca64" (native ARM64).
- To call Python from MATLAB, the Python interpreter must match that architecture (ARM64).
- Using Intel Python (x86_64) with native MATLAB WILL NOT WORK.
- The cleanest solution: use Miniforge3 (Conda-forge's lightweight ARM64 distribution).
===========================================================
1. Install Miniforge3 (ARM64-native Conda)
===========================================================
In Terminal, run:
curl -LO https://github.com/conda-forge/miniforge/releases/latest/download/Miniforge3-MacOSX-arm64.sh
bash Miniforge3-MacOSX-arm64.sh
Follow prompts:
- Press ENTER to scroll through license.
- Type "yes" when asked to accept the license.
- Press ENTER to accept the default install location: ~/miniforge3
- When asked:
Do you wish to update your shell profile to automatically initialize conda? [yes|no]
Type: yes
===========================================================
2. Restart Terminal and Create a Python Environment for MATLAB
===========================================================
Run the following:
conda create -n matlab python=3.10 astropy numpy -y
conda activate matlab
Verify the Python path:
which python
Expected output:
/Users/YOURNAME/miniforge3/envs/matlab/bin/python
===========================================================
3. Verify Python + Astropy From Terminal
===========================================================
Run:
python -c "import astropy; print(astropy.__version__)"
Expected output:
6.x.x (or similar)
===========================================================
4. Configure MATLAB to Use This Python
===========================================================
In MATLAB R2025a (Apple Silicon):
clear classes
pyenv('Version', '/Users/YOURNAME/miniforge3/envs/matlab/bin/python')
py.sys.version
You should see the Python version printed (e.g. 3.10.18). No error means it's working.
===========================================================
5. Gotchas and Their Solutions
===========================================================
❌ Error: Python API functions are not available
→ Cause: Wrong architecture or broken .dylib
→ Fix: Use Miniforge ARM64 Python. DO NOT use Intel Anaconda.
❌ Error: Invalid text character (↑ points at __version__)
→ Cause: MATLAB can’t parse double underscores typed or pasted
→ Fix: Use: py.getattr(module, '__version__')
❌ Error: Unrecognized method 'separation' or 'sec'
→ Cause: MATLAB can't reflect dynamic Python methods
→ Fix: Use: py.getattr(obj, 'method')(args)
===========================================================
6. Run Full Verification in MATLAB
===========================================================
Paste this into MATLAB:
% Set environment
clear classes
pyenv('Version', '/Users/YOURNAME/miniforge3/envs/matlab/bin/python');
% Import modules
coords = py.importlib.import_module('astropy.coordinates');
time_mod = py.importlib.import_module('astropy.time');
table_mod = py.importlib.import_module('astropy.table');
% Astropy version
ver = char(py.getattr(py.importlib.import_module('astropy'), '__version__'));
disp(['Astropy version: ', ver]);
% SkyCoord angular separation
c1 = coords.SkyCoord('10h21m00s', '+41d12m00s', pyargs('frame', 'icrs'));
c2 = coords.SkyCoord('10h22m00s', '+41d15m00s', pyargs('frame', 'icrs'));
sep_fn = py.getattr(c1, 'separation');
sep = sep_fn(c2);
arcsec = double(sep.to('arcsec').value);
fprintf('Angular separation = %.3f arcsec\n', arcsec);
% Time difference in seconds
Time = time_mod.Time;
t1 = Time('2025-01-01T00:00:00', pyargs('format','isot','scale','utc'));
t2 = Time('2025-01-02T00:00:00', pyargs('format','isot','scale','utc'));
dt = py.getattr(t2, '__sub__')(t1);
seconds = double(py.getattr(dt, 'sec'));
fprintf('Time difference = %.0f seconds\n', seconds);
% Astropy table display
tbl = table_mod.Table(pyargs('names', {'a','b'}, 'dtype', {'int','float'}));
tbl.add_row({1, 2.5});
tbl.add_row({2, 3.7});
disp(tbl);
===========================================================
7. Optional: Automatically Configure Python in startup.m
===========================================================
To avoid calling pyenv() every time, edit your MATLAB startup:
edit startup.m
Add:
try
pyenv('Version', '/Users/YOURNAME/miniforge3/envs/matlab/bin/python');
catch
warning("Python already loaded.");
end
===========================================================
8. Final Notes
===========================================================
- This setup avoids all architecture mismatches.
- It uses a clean, minimal ARM64 Python that integrates seamlessly with MATLAB.
- Do not mix Anaconda (Intel) with Apple Silicon MATLAB.
- Use py.getattr for any Python attribute containing underscores or that MATLAB can't resolve.
You can now run NumPy, Astropy, Pandas, Astroquery, Matplotlib, and more directly from MATLAB.
===========================================================
Is it possible to create a Simulink model that is independent of specific microcontrollers?
For example, in the model, the STM32 block is used for CAN transmission. But if I want to deploy the same model to an Arduino, I have to replace the STM32 block with an Arduino-compatible one.
So, is it possible to create a custom block or abstraction that works across multiple microcontrollers like STM32, PIC32, and Arduino without changing the hardware-specific block each time?
Hello,
I've successfully tested the Processor-in-the-Loop (PIL) workflow in Simulink using a TI F28069M LaunchPad, following the standard examples provided by MathWorks. The PIL block, code generation, and communication all worked without issues.
Now, I’d like to run a similar PIL setup using the Infineon TLE9879 EVALKIT (based on an ARM Cortex-M0), which is not officially supported by Simulink as a target.
I’m wondering if it’s possible to configure PIL manually or via custom workflows. For example:
- Can I create a custom PIL target using Embedded Coder?
- Would I need to port rtiostream manually for communication over UART?
- Could I somehow integrate with Keil µVision (which I use for TLE9879) to build and run the generated code?
- Is there a workaround to simulate PIL behavior using a non-supported board?
My setup:
- Simulink R2024b
- Infineon TLE9879 EVALKIT
- Keil µVision 5 + Infineon Config Wizard
- UART and JTAG interfaces available
The main purpose is to validate control algorithms and measure execution time, not to implement a full HIL system.
Has anyone attempted PIL with a custom or unsupported microcontroller before? Any tips or resources would be greatly appreciated. Thanks in advance!
Hi everyone,
Please check out our new book "Generative AI for Trading and Asset Management".
GenAI is usually associated with large language models (LLMs) like ChatGPT, or with image generation tools like MidJourney, essentially, machines that can learn from text or images and generate text or images. But in reality, these models can learn from many different types of data. In particular, they can learn from time series of asset returns, which is perhaps the most relevant for asset managers.
In our book (amazon.com link), we explore both the practical applications and the fundamental principles of GenAI, with a special focus on how these technologies apply to trading and asset management.
The book is divided into two broad parts:
Part 1 is written by Ernie Chan, noted author of Quantitative Trading, Algorithmic Trading, and Machine Trading. It starts with no-code applications of GenAI for traders and asset managers with little or no coding experience. After that, it takes readers on a whirlwind tour of machine learning techniques commonly used in finance.
Part 2, written by Hamlet, covers the fundamentals and technical details of GenAI, from modeling to efficient inference. This part is for those who want to understand the inner workings of these models and how to adapt them to their own custom data and applications. It’s for anyone who wants to go beyond the high-level use cases, get their hands dirty, and apply, and eventually improve these models in real-world practical applications.
Readers can start with whichever part they want to explore and learn from.
Sto tentando inutilmente di salvare il valore dell'enegia che consumo ogni giorno nel field5 di questo canale: https://thingspeak.mathworks.com/channels/2851490 , ma inutilemte in quanto vengono visualizzati sempre e solo 2 dati anche se ho impostato days=30. Ho provato ad aumentare a 365 ma senza variazioni. Come mai?
I am deeply honored to announce the official publication of my latest academic volume:
MATLAB for Civil Engineers: From Basics to Advanced Applications
(Springer Nature, 2025).
This work serves as a comprehensive bridge between theoretical civil engineering principles and their practical implementation through MATLAB—a platform essential to the future of computational design, simulation, and optimization in our field.
Structured to serve both academic audiences and practicing engineers, this book progresses from foundational MATLAB programming concepts to highly specialized applications in structural analysis, geotechnical engineering, hydraulic modeling, and finite element methods. Whether you are a student building analytical fluency or a professional seeking computational precision, this volume offers an indispensable resource for mastering MATLAB's full potential in civil engineering contexts.
With rigorously structured examples, case studies, and research-aligned methods, MATLAB for Civil Engineers reflects the convergence of engineering logic with algorithmic innovation—equipping readers to address contemporary challenges with clarity, accuracy, and foresight.
📖 Ideal for:
— Graduate and postgraduate civil engineering students
— University instructors and lecturers seeking a structured teaching companion
— Professionals aiming to integrate MATLAB into complex real-world projects
If you are passionate about engineering resilience, data-informed design, or computational modeling, I invite you to explore the work and share it with your network.
🧠 Let us advance the discipline together through precision, programming, and purpose.
Bom dia se alguém puder me ajudar, meu código abaixo, não estou conseguintdo conectar o meu Esp8266 ao ThingSpeak, o erro tá na conexão. Estou usando o MicroPython e NodeMCU na plataforma Pytohn o sistema operacional Ubuntu 20
# DHT11 -> ESP8266/ESP32
# 1(Vcc) -> 3v3
# 2(Data) -> GPIO12
# 4(Gnd) -> Gnd
import time, network, machine
from dht import DHT11
from machine import Pin
from umqtt.simple import MQTTClient
print("Iniciando...")
dht = DHT11(Pin(12, Pin.IN, Pin.PULL_UP))
estacao = network.WLAN(network.STA_IF)
estacao.active(True)
estacao.connect('xxxxxxx', 'xxxxxxxxx')
while estacao.isconnected() == False:
machine.idle()
print('Conexao realizada.')
print(estacao.ifconfig())
SERVIDOR = "mqtt.thingspeak.com"
CHANNEL_ID = "XXXXXXXXXXXXXXXXX"
WRITE_API_KEY = "XXXXXXXXXXXXXXXXXXXXX"
topico = "channels/" + CHANNEL_ID + "/publish/" + WRITE_API_KEY
cliente = MQTTClient("umqtt_client", SERVIDOR)
try:
while True:
dht.measure()
temp = dht.temperature()
umid = dht.humidity()
print('Temperatura: %3.1f °C' %temp)
print('Umidade: %3.1f %%' %umid)
conteudo = "field1=" + str(temp) + "&field2=" + str(umid)
print ('Conectando a ThingSpeak...')
cliente.connect()
cliente.publish(topico, conteudo)
cliente.disconnect()
print ('Envio realizado.')
time.sleep(600.0)
except KeyboardInterrupt:
estacao.disconnect()
estacao.active(False)
print("Fim.")
*****************************************************************************************************
No shell aparece como resposta:
MPY: soft reboot
Iniciando...
Conexao realizada.
('192.168.0.23', '255.255.255.0', '192.168.0.1', '8.8.8.8')
Temperatura: 29.0 °C
Umidade: 63.0 %
Conectando a ThingSpeak...
Traceback (most recent call last):
File "<stdin>", line 38, in <module>
File "umqtt/simple.py", line 67, in connect
OSError: -2
linha 38 é cliente.connect()
I want to use Simulink for model-based development of the TC3XX series development board, but I am not sure about the development process and toolchain? Is there a free toolchain available for me to use? Do you have a detailed development tutorial?
I have a pressure vs. time plot resulting from the input of an elastic wave, which I obtained from an Abaqus simulation. So, I have access to all the data. Now, I want to convert this time-domain graph into a frequency-domain graph using FFT in MATLAB.
I came across a code through ChatGPT, but I’m not fully confident in relying on it. Could anyone kindly clarify whether the formulas used for FFT in MATLAB are universal for all types of signals? Or is there a more effective and reliable method I should consider for this purpose?
Hi guys!
Im doing a project where i need to simulate a ship connected to the grid. I have a grid->converter AC-DC-AC -> dynamic load. My converter has to keep the voltage consistent and what changes is the current. Can somebody help me?
I like this problem by James and have solved it in several ways. A solution by Natalie impressed me and introduced me to a new function conv2. However, it occured to me that the numerous test for the problem only cover cases of square matrices. My original solutions, and Natalie's, did niot work on rectangular matrices. I have now produced a solution which works on rectangular matrices. Thanks for this thought provoking problem James.
I wanted to turn a Markdown nested list of text labels:
- A
- B
- C
- D
- G
- H
- E
- F
- Q
into a directed graph, like this:
Here is my blog post with some related tips for doing this, including text I/O, text processing with patterns, and directed graph operations and visualization.
The topic recently came up in a MATLAB Central Answers forum thread, where community members discussed how to programmatically control when the end user can close a custom app. Imagine you need to prevent app closure during a critical process but want to allow the end user to close the app afterwards. This article will guide you through the steps to add this behavior to your app.
A demo is attached containing an app with a state button that, when enabled, disables the ability to close the app.
Steps
1. Add a property that stores the state of the closure as a scalar logical value. In this example, I named the property closeEnabled. The default value in this example is true, meaning that closing is enabled. -- How to add a property to an app in app designer
properties (Access = private)
closeEnabled = true % Flag that controls ability to close app
end
2. Add a CloseRequest function to the app figure. This function is called any time there is an attempt to close the app. Within the CloseRequest function, add a condition that deletes the app when closure is enabled. -- How to add a CloseRequest function to an app figure in app designer
function UIFigureCloseRequest(app, event)
if app.closeEnabled
delete(app)
end
3. Toggle the value of the closeEnabled property as needed in your code. Imagine you have a "Process" button that initiates a process where it is crucial for the app to remain open. Set the closeEnabled flag to false (closure is disabled) at the beginning of the button's callback function and then set it to true at the end (closure is enabled).
function ProcessButtonPress(app, event)
app.closeEnabled = false;
% MY PROCESS CODE
app.closeEnabled = true;
end
Handling Errors: There is one trap to keep in mind in the example above. What if something in the callback function breaks before the app.closeEnabled is returned to true? That leaves the app in a bad state where closure is blocked. A pro move would be to use a cleanupObj to manage returning the property to true. In the example below, the task to return the closeEnabled property to true is managed by the cleanup object, which will execute that command when execution is terminated in the ProcessButtonPress function—whether execution was terminated by error or by gracefully exiting the function.
function ProcessButtonPress(app, event)
app.closeEnabled = false;
cleanupClosure = onCleanup(@()set(app,'closeEnabled',true));
% MY CODE
end
Force Closure: If the CloseRequest function is preventing an app from closing, here are a couple of ways to force a closure.
- If you have the app's handle, use delete(app) or close(app,'force'). This will also work on the app's figure handle.
- If you do not have the app's handle, you can use close('all','force') to close all figures or use findall(groot,'type','figure') to find the app's figure handle.
I have written, tested, and prepared a function with four subsunctions on my computer for solving one of the problems in the list of Cody problems in MathWorks in three days. Today, when I wanted to upload or copy paste the codes of the function and its subfunctions to the specified place of the problem of Cody page, I do not see a place to upload it, and the ability to copy past the codes. The total of the entire codes and their documentations is about 600 lines, which means that I cannot and it is not worth it to retype all of them in the relevent Cody environment after spending a few days. I would appreciate your guidance on how to enter the prepared codes to the desired environment in Cody.
Me: If you have parallel code and you apply this trick that only requires changing one line then it might go faster.
Reddit user: I did and it made my code 3x faster
Not bad for just one line of code!
Which makes me wonder. Could it make your MATLAB program go faster too? If you have some MATLAB code that makes use of parallel constructs like parfor or parfeval then start up your parallel pool like this
parpool("Threads")
before running your program.
The worst that will happen is you get an error message and you'll send us a bug report....or maybe it doesn't speed up much at all....
....or maybe you'll be like the Reddit user and get 3x speed-up for 10 seconds work. It must be worth a try...after all, you're using parallel computing to make your code faster right? May as well go all the way.
In an artificial benchmark I tried, I got 10x speedup! More details in my recent blog post: Parallel computing in MATLAB: Have you tried ThreadPools yet? » The MATLAB Blog - MATLAB & Simulink
Give it a try and let me know how you get on.
I am pleased to announce the 6th Edition of my book MATLAB Recipes for Earth Sciences with Springer Nature
also in the MathWorks Book Program
It is now almost exactly 20 years since I signed the contract with Springer for the first edition of the book. Since then, the book has grown from 237 to 576 pages, with many new chapters added. I would like to thank my colleagues Norbert Marwan and Robin Gebbers, who have each contributed two sections to Chapters 5, 7 and 9.
And of course, my thanks go to the excellent team at the MathWorks Book Program and the numerous other MathWorks experts who have helped and advised me during the last 30+ years working with MATLAB. And of course, thank you Springer for 20 years of support.
This book introduces methods of data analysis in the earth sciences using MATLAB, such as basic statistics for univariate, bivariate, and multivariate data sets, time series analysis, signal processing, spatial and directional data analysis, and image analysis.
Martin H. Trauth
Hello ThingSpeak Community,
I have an energy meter sending data of energy consumed in 4 rooms in hexadecimal values to Sigfox and I was trying to decode the payload and route it to ThingSpeak.
All the datas are sent at the same time.
But ThingSpeak only receives 1 of them and plots them.
However, the rest 3 are missing. Is this because I am trying the free version ?
Would the payed version be capable of receiving all the 4 messages ?
I am glad to inform and share with you all my new text book titled "Inverters and AC Drives
Control, Modeling, and Simulation Using Simulink", Springer, 2024. This text book has nine chapters and three appendices. A separate "Instructor Manual" is rpovided with solutions to selected model projects. The salent features of this book are given below:
- Provides Simulink models for various PWM techniques used for inverters
- Presents vector and direct torque control of inverter-fed AC drives and fuzzy logic control of converter-fed AC drives
- Includes examples, case studies, source codes of models, and model projects from all the chapters
The Springer link for this text book is given below:
This book is also in the Mathworks book program:
The GCD approach to identify rough numbers is a terribly useful one, well worth remembering. But at some point, I expect someone to notice that all work done with these massively large symbolic numbers uses only one of the cores on your computer. And, having spent so much money on those extra cores in your CPU, surely we can find a way to use them all? The problem is, computations done on symbolic integers never use more than 1 core. (Sad, unhappy face.)
In order to use all of the power available to your computer using MATLAB, you need to work in double precision, or perhaps int64 or uint64. To do that, I'll next search for primes among the family 3^n+4. In fact, they seem pretty common, at least if we look at the first few such examples.
F = @(n) sym(3).^n + 4;
F(0:16)
ans =
[5, 7, 13, 31, 85, 247, 733, 2191, 6565, 19687, 59053, 177151, 531445, 1594327, 4782973, 14348911, 43046725]
isprime(F(0:16))
ans =
1×17 logical array
1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0
Of the first 11 members of that sequence, 7 of them were prime. Naturally, primes will become less frequent in this sequence as we look further out. The members of this family grow rapidly in size. F(10000) has 4771 decimal digits, and F(100000) has 47712 decimal digits. We certainly don't want to directly test every member of that sequence for primality. However, what I will call a partial or incomplete sieve can greatly decrease the work needed.
Consider there are roughly 5.7 million primes less than 1e8.
numel(primes(1e8))
ans =
5761455
F(17) is the first member of our sequence that exceeds 1e8. So we can start there, since we already know the small-ish primes in this sequence.
roughlim = 1e8;
primes1e8 = primes(roughlim);
primes1e8([1 2]) = []; % F(n) is never divisible by 2 or 3
F_17 = double(F(17));
Fremainders = mod(F_17,primes1e8);
nmax = 100000;
FnIsRough = false(1,nmax);
for n = 17:nmax
if all(Fremainders)
FnIsRough(n) = true;
end
% update the remainders for the next term in the sequence
% This uses the recursion: F(n+1) = 3*F(n) - 8
Fremainders = mod(Fremainders*3 - 8,primes1e8);
end
sum(FnIsRough)
ans =
6876
These will be effectively trial divides, even though we use mod for the purpose. The result is 6876 1e8-rough numbers, far less than that total set of 99984 values for n. One thing of great importance is to recognize this sequence of tests will use an approximately constant time per test regardless of the size of the numbers because each test works off the remainders from the previous one. And that works as long as we can update those remainders in some simple, direct, and efficient fashion. All that matters is the size of the set of primes to test against. Remember, the beauty of this scheme is that while I did what are implicitly trial divides against 5.76 million primes at each step, ALL of the work was done in double precision. That means I used all 8 of the cores on my computer, pushing them as hard as I could. I never had to go into the realm of big integer arithmetic to identify the rough members in that sequence, and by staying in the realm of doubles, MATLAB will automatically use all the cores you have available.
The first 10 values of n (where n is at least 17), such that F(n) is 1e8-rough were
FnIsRough = find(FnIsRough);
FnIsRough(1:10)
ans =
22 30 42 57 87 94 166 174 195 198
How well does the roughness test do to eliminate composite members of this sequence?
isprime(F(FnIsRough(1:10)))
ans =
1×10 logical array
1 1 1 1 1 0 0 1 1 1
As you can see, 8 of those first few 1e8-rough members were actually prime, so only 2 of those eventual isprime tests were effectively wasted. That means the roughness test was quite useful indeed as an efficient but relatively weak pre-test for possible primality. More importantly it is a way to quickly eliminate those values which can be known to be composite.
You can apply a similar set of tests on many families of numbers. For example, repunit primes are a great case. A rep-digit number is any number composed of a sequence of only a single digit, like 11, 777, and 9999999999999.
However, you should understand that only rep-digit numbers composed of entirely ones can ever be prime. Naturally, any number composed entirely of the digit D, will always be divisible by the single digit number D, and so only rep-unit numbers can be prime. Repunit numbers are a subset of the rep-digit family, so numbers composed only of a string of ones. 11 is the first such repunit prime. We can write them in MATLAB as a simple expression:
RU = @(N) (sym(10).^N - 1)/9;
RU(N) is a number composed only of the digit 1, with N decimal digits. This family also follows a recurrence relation, and so we could use a similar scheme as was used to find rough members of the set 3^N-4.
RU(N+1) == 10*RU(N) + 1
However, repunit numbers are rarely prime. Looking out as far as 500 digit repunit numbers, we would see primes are pretty scarce in this specific family.
find(isprime(RU(1:500)))
ans =
2 19 23 317
There are of course good reasons why repunit numbers are rarely prime. One of them is they can only ever be prime when the number of digits is also prime. This is easy to show, as you can always factor any repunit number with a composite number of digits in a simple way:
1111 (4 digits) = 11*101
111111111 (9 digits) = 111*1001001
Finally, I'll mention that Mersenne primes are indeed another example of repunit primes, when expressed in base 2. A fun fact: a Mersenne number of the form 2^n-1, when n is prime, can only have prime factors of the form 1+2*k*n. Even the Mersenne number itself will be of the same general form. And remember that a Mersenne number M(n) can only ever be prime when n is itself prime. Try it! For example, 11 is prime.
Mn = @(n) sym(2).^n - 1;
Mn(11)
ans =
2047
Note that 2047 = 1 + 186*11. But M(11) is not itself prime.
factor(Mn(11))
ans =
[23, 89]
Looking carefully at both of those factors, we see that 23 == 1+2*11, and 89 = 1+8*11.
How does this help us? Perhaps you may see where this is going. The largest known Mersenne prime at this date is Mn(136279841). This is one seriously massive prime, containing 41,024,320 decimal digits. I have no plans to directly test numbers of that size for primality here, at least not with my current computing capacity. Regardless, even at that realm of immensity, we can still do something.
If the largest known Mersenne prime comes from n=136279841, then the next such prime must have a larger prime exponent. What are the next few primes that exceed 136279841?
np = NaN(1,11); np(1) = 136279841;
for i = 1:10
np(i+1) = nextprime(np(i)+1);
end
np(1) = [];
np
np =
Columns 1 through 8
136279879 136279901 136279919 136279933 136279967 136279981 136279987 136280003
Columns 9 through 10
136280009 136280051
The next 10 candidates for Mersenne primality lie in the set Mn(np), though it is unlikely that any of those Mersenne numbers will be prime. But ... is it possible that any of them may form the next Mersenne prime? At the very least, we can exclude a few of them.
for i = 1:10
2*find(powermod(sym(2),np(i),1+2*(1:50000)*np(i))==1)
end
ans =
18 40 64
ans =
1×0 empty double row vector
ans =
2
ans =
1×0 empty double row vector
ans =
1×0 empty double row vector
ans =
1×0 empty double row vector
ans =
1×0 empty double row vector
ans =
1×0 empty double row vector
ans =
1×0 empty double row vector
ans =
2
Even with this quick test which took only a few seconds to run on my computer, we see that 3 of those Mersenne numbers are clearly not prime. In fact, we already know three of the factors of M(136279879), as 1+[18,40,64]*136279879.
You might ask, when is the MOD style test, using a large scale test for roughness against many thousands or millions of small primes, when is it better than the use of GCD? The answer here is clear. Use the large scale mod test when you can easily move from one member of the family to the next, typically using a linear recurrence. Simple such examples of this are:
1. Repunit numbers
General form: R(n) = (10^n-1)/9
Recurrence: R(n+1) = 10*R(n) + 1, R(0) = 1, R(1) = 11
2. Fibonacci numbers.
Recurrence: F(n+1) = F(n) + F(n-1), F(0) = 0, F(1) = 1
3. Mersenne numbers.
General form: M(n) = 2^n - 1
Recurrence: M(n+1) = 2*M(n) + 1
4. Cullen numbers, https://en.wikipedia.org/wiki/Cullen_number
General form: C(n) = n*2^n + 1
Recurrence: C(n+1) = 4*C(n) + 4*C(n-1) + 1
5. Hampshire numbers: (My own choice of name)
General form: H(n,b) = (n+1)*b^n - 1
Recurrence: H(n+1,b) = 2*b*H(n-1,b) - b^2*H(n-2,b) - (b-1)^2, H(0,b) = 0, H(1,b) = 2*b-1
6. Tin numbers, so named because Sn is the atomic symbol for tin.
General form: S(n) = 2*n*F(n) + 1, where F(n) is the nth Fibonacci number.
Recurrence: S(n) = S(n-5) + S(n-4) - 3*S(n-3) - S(n-2) +3*S(n-1);
To wrap thing up, I hope you have enjoyed this beginning of a journey into large primes and non-primes. I've shown a few ways we can use roughness, first in a constructive way to identify numbers which may harbor primes in a greater density than would otherwise be expected. Next, using GCD in a very pretty way, and finally by use of MOD and the full power of MATLAB to test elements of a sequence of numbers for potential primality.
My next post will delve into the world of Fermat and his little theorem, showing how it can be used as a stronger test for primality (though not perfect.)
