I am a student studying IT in an University. I've been giving an assignment of searching for prime numbers above one quadrillion. Steps have been given:
Start number as one quadrillion
Select odd-numbered candidates
Divide them by every odd integer between 3 and their square root. if one of the integers evenly divides the candidate, it's declared prime.
Now this is what i've come up with :
import java.io.*;
import javax.servlet.*;
import javax.servlet.http.*;
public class PrimeSearcher extends HttpServlet{
private long number = 10000000000000001L;
private boolean found = false;
public void doGet(HttpServletRequest request, HttpServletResponse response) throws IOException, ServletException {
PrintWriter out = response.getWriter();
while(!checkForPrime(number)){
number = number+2;
}
if(found){
out.println("The first prime number above 1 quadrillion is : " + number);
}
}
public boolean checkForPrime(long numberToCheck){
double sqrRoof = Math.sqrt(numberToCheck);
for(int i=3; i< sqrRoof; i++){
if(numberToCheck%i==0){
return false;
}
}
found= true;
return found;
}
}
My worry is that am not sure whether am on the right path and another issue is that this always one number ,the first one. after googling i found that on servlet.com and javafaq that they are using thread and i've run theirs and it seem to be cool. I don't really understand that one but it gives different numbers.
So I am now confused right now about how to implement that algorithm and i really don't want to copy that one. Maybe after understanding their method i can code this algorithm better.
Thanks
I think it looks OK, but you might need the i
in checkForPrime
to be a long
type. And you're not incrementing i
by 2 (you only need to check for odd divisors).
Just be prepared for this to take a long time.......
此外,您需要checkForPrime
直到i<=sqrRoof
(sqrRoof可能是一个整数)。
you have 10 quadrillion written in your source code, not one quadrillion. Just so you know. :)
In case you need them, primes above one quadrillion are:
37,91,159,187,223 ...
Above 10 quadrillion:
61,69,79 ...
The standard way to check a large prime is to generate a list of low primes, up to some limit, using the Sieve of Eratosthenes. Use that list to check odd numbers in the quadrillion range, to eliminate most non-primes.
Then use the Miller-Rabin probabilistic prime test to check if any remaining large number really is prime. If you repeat the MR test up to 64 times, then there is a far larger chance that your hardware has failed than that you have inadvertently found a composite number.
The MR test is much faster than trial division for large numbers.
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