How big are primes?

So, If we were to calculate the first billion primes how much ram would we need?
At the end the primes won't fit in a 32bit integer. If we store them all in 64bit integers we'd need 8GB.
Even if they all fit in 32bit integers we'd still need 4GB of storage just to store the list.

Seeing at my little machine has 4GB ram that isn't going to work either.

How about just storing the intervals between primes?
For the first primes (2, 3, 5, 7, 11, 13, 17) we would store (2, 1, 2, 2, 4, 2, 4)

Using a byte for every interval less than 128 and a short for the rest lets us store the first billion primes in just about 1GB. Now that we can do!

Maybe we can do even better though...

Comments

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...

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!

Segmented Sieve

Our next version works just like the previous sieve but works on a segment of the number line at a time. That might be why it is called a segmented sieve . Now we are sieving multiples of the primes from 1M numbers at a time, adding those primes to the list and then moving on to the next 1M numbers. I hit 140M primes in 60 seconds on my box... but now I run into a new problem. This version of the sieve quickly consumes all the memory in my box and slows to a crawl. To progress we will need to find a more efficient way of storing the primes we have found.

Programmers Dojo

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