Skip to main content

A Prime Vacation

I like to do small programming exercises to keep my skills sharp.  Unfortunately I sometimes get a little carried away with them.

Problem: generate a list of primes numbers.

Sounds simple right?  Well lets start to look at this.  First lets define what prime numbers are.  A prime number is a number which is divisible by only itself and one.  A simple way to test if a number if prime is by trial division.  To test to see if a number is prime you check whether it is division by any prime less then the square root of that number.

The general algorithm for finding the list of primes by trial division is therefore the following.

list of primes = {2, 3}
for each number begining at 4
  check to see if it is divisible by any prime less then the square root of number
  if number is prime then append it to list of primes

Well go through a sample implementation then see what we can do to improve it.
Labels:

Comments

Post a Comment

Popular posts from this blog

Duck typing considered harmful.

I've had a chance to work on a fairly large chunk of Python at this point and have decided that Python (like Perl) is completely untenable at scale.  <rant><rave><drool>  but wait!  I have reasons! Programmers spend most of their time reading code.  We read massive amounts of code.  After we read massive amounts of code we write one... or change one... To make a change to a piece of code you first have to understand what it does and how it interacts with the system around it.  Then we start reading massive amounts of code again.  Anything you can do to minimize the amount of code a programmer has to understand to make a change becomes a huge gain in productivity. Duck typing causes the amount of code you need to read to make a change to grow very large. For example lets look at two functions, one in C++ and one in Python. First in C++ int function(type1 arg1, type2 arg2) {   return arg1->method(arg2); } In this fun...
1 comment
Read more

Types of arrays

Arrays are one of the earliest data structures.  They are essentially just a block of memory which is accessed by offset.  Despite their simplicity there are still several broad categories each with their own sets of algorithms. Is the array a fixed size or can it grow as you add elements to it? A fixed size array is called a static array and one that can grow is called a dynamic array. Are the element all of the same type or can they be different? If they must all be the same type then the array are called homogeneous.  Otherwise it is a heterogeneous array. Finally, how many dimensions (subscripts) does the array have? For example, a 2 dimensioned array is a matrix. The number of dimensions doesn't change the structure of the array but changes the way elements are accessed. 
2 comments
Read more

Tamiya Tracks

So... a "buddy" of mine got me this for Christmas this year.   I figure... hey, what the heck!  I should be able to get in trouble with this! It makes a nice little vehicle that works quite well.  I hope to turn this into a cool little telepresence rover but during the course of assembly I realized something... No "friend" should every give you something with pieces like this! I am seriously not built for handling pieces that small!
Post a Comment
Read more