Larry Deering, W2GL
w2gl@qsl.net

updated March 8, 2001

Below are links to: the Black Key Sieve, an improvement on the Sieve of Erastothenes (fastest on the internet), a Mandelbrot program I wrote, a program for Barker Codes, and a TiCK Keyer modification.

Download Barker.cpp, a program for finding Barker codes to 32 bits, the results in a text fileBarkcode.txt, Barkcode.zip, or the program itself, Barker.exe. Barker codes are codes that have very good autocorrelation response, and are often used in radar, planetary ranging, or other high noise low signal environments.

Download Fastman, a Mandelbrot program I wrote! The challenge was to write a program disproving the statement that every point in a chaotic plot had to be calculated. The features of this program include: contour following using a spatial filter, a suite of plot coordinates, and programming in C with lots of assembly routines for speed. You'll need a 386 with a 387 math coprocessor or better, and DOS with a VGA monitor. This isn't nearly as comprehensive a program as Fractint. It's a lot smaller (the exe is 45,761 bytes), zipped with instructions is 33,176 bytes vs. 602,624 bytes for FRAIN195.zip (which expands to 2,085,582 bytes). It runs very fast, and is interesting to watch.

I wrote a prime number program called the "Black Key Sieve" derived from the Sieve of Eratosthenes. It's more efficient in computation and storage space than standard sieves. Now that my computer is a 6x86 Cyrix running at 200 MHz, it reports calculation time for numbers to 100,000,000 as either two or three seconds. It will calculate and store the sieve on hard disk in about five seconds. This is a lot faster than the 286 the program was developed on, and timer granularity of a second used to be acceptable. The next update will report in milliseconds.

The sieve is more efficient because it's compressed. For example, a 3,335,332 byte field represents all of the prime numbers through 100,059,960. The sample program works on 17017 bytes at a time, and concatenates the current field to the fields already on disk. An interesting feature is use of large palindromes to cancel non-primes. Part of this description is how to work on compressed fields, and how to use very large base numbers for efficiency.

The name is from analyzing of the Sieve of Eratosthenes while watching my mother play piano. The analog is a sieve arranged like a piano, where keys represent numbers. Listen to a long piano composition while watching the pianist strike the keys. Say white keys are numbers with low factors, and the black keys represent numbers without those factors. Every time a white key is struck, time is wasted. My remedy is to build a piano with only black keys, and an algorithm to strike the notes. It's not hard, once you know the chords. There's a longer description mostly from an unpublished article from '93. If you like, read the description now, or download the program Blackkey.exe. Many thanks to Herb Savage for verification of the prime count report of 5,764,694 primes found. The real number is three higher; the sieve does not contain 2,3, or 5, so they are not counted.

73 and Good Luck!
Larry Deering, w2gl
Bellport NY