I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them - Mark Haddon, The Curious Incident of the Dog in the Night-Time

At some point, I realize I consider the Circuit Playground kind of a multi-tool - sensors, inputs, sound output, control of motors and more... actually, maybe more like Doctor Who's Sonic Screwdriver....

This week I worked to reconfigure my CPX to search for prime numbers because... why not? With my memory of the Sieve of Eratosthenes it took no time to find Python code to adapt for CircuitPython. In fact the code pretty much ran fine from the start. 

First though, I made a version for Makecode - essentially using the Python code as a model. And then I made the CircuitPython version - actually two versions. More on that later. (And, yes, there is a NeoTrinkey version as well).

It is all in this repository : Eratosthenes

• ESieve.js - MakeCode/Javascript for finding all primes < 1000 https://makecode.com/_H5qFx46rYF1c for Makecode version
• ESieve.py - CircuitPython for finding all primes < 1000 - copy to code.py
• ESievePlus.py - CircuitPython for finding all primes < 8000 - copy to code.py

All three of the above will flash colored lights while searching for the prime numbers. When done, A will pick a random prime and display it, first in binary, then digit-by-digit in decimal version. Pressing B will step through all of the primes it found, displaying in binary. Touch A1 to display the last random prime it found in the random selection from pressing A.

The coding of binary values uses the ten neopixels - Green for 1's and Blue for 0's

NeoPixel:  0    1    2    3    4     5    6      7     8    9

Value:        1    2    4   8   16   32  64  128 256 512

The digit-by-digit display of a number lights up yellow pixels to show a value, with the rest of the pixels blue (so for 0 they all are blue).

• neosieve.py - neotrinkey version (copy to code.py)
• ncount.py - support file for neosieve.py

NeoTrinkey version. It finds all primes < 1000. First it flashes colored lights while searching, then, when done, touching pad #1 will display a random prime digit by digit with binary coding. Touching pad #2 will redisplay the last random prime found.

The "digits" displayed use the binary coding I had in the RRPN Calculator project:

All of the Circuit Python versions (neotrinkey or Circuit Playground), if connected to Mu or a similar IDE, will print information to the REPL.

Code based on https://www.geeksforgeeks.org/python-program-for-sieve-of-eratosthenes/ - MakeCode version written from scratch recreating the algorithm followed in that sample Python code.

Challenges

It seemed ... paltry to ONLY do the primes < 1000 but creating a Boolean array of more than 1000 ran into memory limitations. To fix that, in ESievePlus.py, instead of an array of Booleans,  I created an array of 1000 8 bit numbers, initially set to 255 (11111111 in binary) and wrote functions to clear bits (indicating NOT prime) and another to test whether individual bits were 1 (prime) or 0 (not prime).

This introduced another problem - numbers greater than 1023 need more than 10 bits to display - so I modified the showbin() routine to shift all the pixels when displaying the higher bits.

Note: Since it takes a while to display hundreds of prime numbers when you push the B button (over a thousand for the ESievePlus.py version!) - the A button is an easy way to sample the primes that were found.