./prime-plot [options]
--help Displays this information
--action=<action> Specify the action the program will execute.
These are the supported values for <action>:
generate
Generate all primes up to the specified limit in
the specified base and output them.
last-digit-ascii-art
Check all primes up to the specified limit in the
specified base for their last digit and output
the number of combinations for consecutive primes
in an ascii art table. The left column will
contain the first value of the combination (the
'from' number), the top row will contain the
second value (the 'to' number). Note that all
information the table contains will be in base
10.
last-digit-csv
Like last-digit-ascii-art, but uses comma
separated values for output and will not contain
any headers.
last-digit-csv-with-headers
Like last-digit-csv, but output will include
headers embedded into the 'useful' output.
diagonal-averages
Output the averages of all diagonals, from bottom
left to top right, of the table generated by any
last-digit-* action. E.g. when --base=3, the rows
(with the 'from' numbers) are from 0 to 2, the
columns (with the 'to' numbers) have the same
range. The first number output by this action will
then be the 2-->0 number. The second will be the
average of the 2-->1 and 1-->0 numbers. The third
will be the average of the 2-->2, 1-->1 and 0-->0
numbers and so on. Eventually, this will lead to
2*base-1 output numbers.
plot-diagonal-averages
Uses the output of diagonal-averages (by
internally calling) it and plots it in a cartesian
coordinate system with the index of the diagonal
average on the x-axis and the value of the
diagonal average on the y-axis. The size of the
coordinate system can be changed using the
--terminal-size option. If that option is not
given, and you are on a Unix operating system, the
current terminal size is read using platform-
dependent commands so that the coordinate system
will fit the terminal exactly. Note that your
terminal has to support Unicode characters for
correctly showing the output of this action,
because the representation of individual pixels is
realized using Braille characters.
This option is required.
--base=<base>[,<alphabet>] Set the base to use for primes during processing.
Note that this option will not change the base of the
number of combination output by last-digit-* actions.
However, it does change the base of primes output by
the generate action. The alphabet is optional with a
default value of 0123456789, but if it is given, it has
to be a string that is 'base' characters long and that
contains the alphabet used for outputting numbers. As
an example, you may use
--base=26,ABCDEFGHIJKLMNOPQRSTUVWXYZ if you want to
output the primes in base 26 with letters as numbers.
If this option is not given, base 10 with 0123456789 as
alphabet is used.
--limit=<limit> Set the limit for the number of primes to test (not the
primes themselves!). When the value has a K, M, G or T
prefix, it will be multiplied by a thousand, a million,
a billion or a trillion, respectively. This option is
required.
--output=<file> Sets the filename of the file used for output. If this
option is not given, the standard output is used.
--prime-input=<file>[,<begin_index>] When a valid file is specified for
this option, the primes needed for the desired action
will be read from it (for 'generate' as well). If
this option is not given, all of the needed primes
will be generated again at runtime. When a value for
'limit' is specified and the specified input file
does not contain all needed primes, the missing ones
will be generated as well. The begin index is not
necessary for this option (its default value is 0,
because the first line is expected to contain 2), but
if it is given, it specifies the index of the first
prime in the file (zero-based), e.g. the begin index
for this option should be 1233 if the first line in
the file contains 10061.
--prime-input-base=<base>[,<alphabet] Expects the same parameters as
--base, but controls the base of the primes read from
the file specifies by --prime-input. If this option is
not given, base 10 with 0123456789 as alphabet is used.
--row-interval=i,j Only output every jth row, beginning at row i. The row
numbers are zero-based. E.g. when this option's value
is 2,3, the program will output the rows #2, #5, #8
and so on. The default value for this option is 0,1.
--column-interval=i,j Works just like --row-interval, just for columns. The
default value for this option is 0,1 as well.
--enable-ascii-art-colors=y/n If this option's value begins with 'n' or '0',
and --action=last-digit-ascii-art, the background of
the numbers in the table body will be colored. If a
value is the highest in the table, it will be colored
in bright red, linearly going down to white, i.e. 0.
Note that ANSI escape sequences are used to color the
background in true color (ISO-8613-3), your terminal
may not support this. Recent versions of Xterm, GNOME
terminal, KDE's Konsole and the OS X terminal should
support this, others may or may not, and Windows's
CMD does not at all. When the output is redirected
to a file using --output, this option is ignored and
no colors are used. By default, this option is disabled.
--terminal-size=width,height If the application is used on a Unix system
and the plot-diagonal-averages action is used, this
option is optional, otherwise it is required.
This option expects the width and height of the terminal
it runs in in a number of simple characters.
./prime-plot --action=generate --limit=10K./prime-plot --action=generate --limit=10K --base=26,ABCDEFGHIJKLMNOPQRSTUVWXYZ./prime-plot --action=generate --limit=1M --output=primes1m.txt./prime-plot --action=last-digit-ascii-art --limit=100K./prime-plot --action=last-digit-ascii-art --limit=100K --enable-ascii-art-colors=y --base=16 --row-interval=1,2 --column-interval=1,2./prime-plot --action=plot-diagonal-averages --prime-input=primes1m.txt --limit=100K./prime-plot --action=plot-diagonal-averages --prime-input=primes1m.txt --limit=100K --base=128 --row-interval=1,2 --column-interval=1,2
I actually got the idea for this program from this Numberphile video where the amazing Dr. James Grime explains patterns in the last digits of primes. Just for fun, I wanted to take this a step further and explore these patterns in other bases as well. For a non-mathematician like me, the arising patters were very surprising. And because Linux terminals support the entire RGB set, it is possible to plot them with a lot of color! When you have access to a non-Windows machine, you should really try out these examples! For your convenience, I kept the executable file in the bin directory, but of course, if you have the neccessary tools, you can do make clean && make.