I'm struggling with primes...
I want to create a calculation program which need to check a number to be prime.
No problem so far!
The problem starts when this number exceeds 48 million.
The way my programming will start calculating primes is as following:
- Skip 0 and 1.
- Print 2, as it is the only even prime number
- Start counting from 3 and skip all even numbers.
So far I used this method:
- Get the root of the number to check
- Get the remainder of the number when diving by all odd numbers till the root has been reached.
As you can guess this is pretty slow...
The reason I do not use sieves is because they are limited! I bet no one can calculate a number higher then 250 trillion to be prime with the sieve of eratosthenes. No computer can create a list counting till that number and start strikethrough numbers...
There is one choice I still have to make... Am I going to store the primes or not.
If I do I can use them to quicken the calculation process, but it will reach it limit after a few million numbers...
I was thinking of using the sieve of eratosthenes till 20 million has been reached and then jump over to another method.
The main goal is to be able to calculate primes starting at any given number till eternity.
I founded out myself that I won't be able to use the following methods for my main goal:
- Sieve of eratosthenes (only partially)
- Sieve of Atkin (only partially)
- Mersenneprime with Lucas-Lehmertest
Please correct me if I'm wrong! And tell me then why I can use these methods.
So my question is:
How to calculate an unknown prime (since it has no limit).
Thanks in advance,
I will check out the combination of Miller-Rabin with AKS.