The Prime Hexagon is a simple mathematical structure that appears when integers are sequentially added to a field of tessellating equilateral triangles, provided the path of the integers is altered each time a prime number appears.
This code computes prime numbers, their positons in the prime hexagon, the polarity of the number, and the prime hexagon's overall rotation. For more information go to hexspin.com. Youtube:https://www.youtube.com/watch?v=fQL4KRH3wUQ
Compute the first set of output values
python ./primespin.py --nvalues=10000000 --chunks 100
Resume a computation given a saved file:
python ./primespin.py --startfile ./output-00000000000000107000-00000000000000108000.npz --chunks 100
TODO
Run with the --help argument to see the help file.
python primespin.py --help
usage: primespin.py [-h] [--infile INFILE] [--viewvalues VIEWVALUES]
[--find FIND] [-c] [--dir DIR] [--basename BASENAME]
[--logfile LOGFILE] [--verbose VERBOSE] [--save-text]
[--save-binary] [--use-cython] [--no-use-cython]
[--nvalues NVALUES] [--skip SKIP] [--chunks CHUNKS]
Prime Spin Hexagons
optional arguments:
-h, --help show this help message and exit
--infile INFILE Input file to start processing chunks
--viewvalues VIEWVALUES
Values to view in the file as a python slice, e.g.
1:100:
--find FIND Find values in files
-c, --compress flag to indicate whether or not to compress output
files
--dir DIR Directory to read/write files to
--basename BASENAME Basename of files to read and write
--logfile LOGFILE Save messagse to this log file
--verbose VERBOSE Print messages to the terminal
--save-text Flag to save text files
--save-binary Flag to save binary files
--use-cython Flag to use cython implementation if available
--no-use-cython Flag to not use cython implementation
--nvalues NVALUES number of values to process in a chunk
--skip SKIP number of values to skip in printing output
--chunks CHUNKS number of chunks to processHere are a few sample command lines:
Generate 1000 files of 1B values each
primespin.py --nvalues=1000000000 --chunks=1000
or
python3 primespin.py --nvalues=$(echo 10,000,000,000 | tr -d ,) --chunks=10000 --skip=0 --logfile run.log
Same thing but write out only every 1Mth value:
primespin.py --nvalues=10000000000 --chunks=10 --skip=0
Now resume a computation starting at the specified file:
primespin.py --chunks=10 --skip=0 --infile output-00000000009000000000-00000000010000000000.npz
It turns out we don't always want to print out all the values we are computing. In fact, if we just want to be able to resume computations, we only need the last set of values in a range stored.
Use --skip=0 to save only a single value - the last set of values in the range.
--skip=1 is also valid to print out all values in the range.
But any other value is not going to work if you want to use chunks.
Print some values from the binary .npz files
primespin.py --viewvalues=:: --infile output-00000000009000000000-00000000010000000000.npz
Note viewvalues is evaluated as an extended Python slice. That is, the values are
start:stop:step
Also any of those values can actually be negative values to indicate starting from the other end in the case of start and stop. If you make step negative it counts backward.
So let's print the last value in this file:
primespin.py --viewvalues=-1:: --infile output-00000000009000000000-00000000010000000000.npz
the --find argument takes a comma separated list of values. The program looks through the output directory for all files. The program searches for numbers and prints the surrounding prime hexagon values.
python primespin.py --find 2004698834,2005554573,8999550398
2015-11-30 00:32:46,658 - prime_hexagon - INFO - using numpy primehexagon implementation
2015-11-30 00:32:46,658 - prime_hexagon - INFO - looking for files matching pattern output/output-[0-9]*-[0-9]*.npz
2015-11-30 00:32:46,659 - prime_hexagon - INFO - found 10 files
(2004484351, 1, -1, 1145)
(2004698833, 1, -1, 1126)
----> 2004698834 <----
(2009838559, 3, -1, 1113)
(2010052483, 5, -1, 1115)
(2005341167, 0, 1, 1126)
(2005554553, 1, -1, 1146)
----> 2005554573 <----
(2011554973, 5, -1, 1131)
(2011769437, 1, -1, 1118)
(8999319293, 4, 1, 2052)
(8999550397, 1, -1, 2052)
----> 8999550398 <----the tests/ directory has some tests. To run them, you'll need to
pip install py.test
PYTHONPATH=. py.test -v --debug tests/test_prime_hex.py