532 Prime Grid

[Mini-Geek]

Originally Posted by spkarra

I used BigInteger.IsProbablePrime(int certainity).

This isn't proving primes, this is showing that the number is a probable prime. The likelihood of a random PRP being composite is ridiculously low, but mathematically it's important.
http://en.wikipedia.org/wiki/Probable_prime

Originally Posted by spkarra

To baseline my tests, I ran with the know Primes.

For Mersenne Prime 2^9941 - 1 (2993 digits long) the above Java Function took 2mins 47 secs.
For 2^11213-1 (3376) it took 4mins.
For 2^21701 - 1(6533) it took 29 mins 28 secs.
For 2^44497 - 1 (13395), NOTHING resulted even after running for 2 hrs.

That means, with the computing capacity that I have, I will try to find the 532 Grid upt0 7000 digits long.

As of today, I did upto 4500 digits.

PFGW can show that 2^44497-1 is PRP in about a second, (though even better methods exist for Mersenne numbers) and 5*3^54287-2 (25903 digits, if I'm right) in about 6 seconds. While it can still be an interesting and informative experience to make all this through Java, it is not an efficient use of your computing capacity.
Without any advance sieving, (just some prefactoring on each number with the -f100 argument) I can search all PRPs up to n=10k (should be 4772 digits) in about 9 minutes. (primes/PRPs found from this attached, for those unfamiliar, primes are in pfgw-prime.log and PRPs are in pfgw.log; these primes were found because they were so small it was easier to trivially prove them prime by trial division than to run a PRP test)
This is the file used in PFGW:

ABC2 5*3^$a$b
a: from 1 to 10000
b: in { -2 +2 }

If you save that as 10k.txt, then run Win32PFGW.exe and put in "10k.txt -f100" it will find all PRPs in that range. But note that they are PRPs only, and not proven. Since the numbers plus or minus one are not trivially factored, to know that they are actually prime requires a difficult test using Primo. Of course, you can change the n bounds to whatever you want.
You could probably speed the search significantly by sieving in advance using a program like srsieve, then giving the sieved file to PFGW and not using the -f100 command. I suspect that this is how Batalov has continued the search into the tens of thousands of digits, which certainly wouldn't be very fast (if possible) with Java.

[Batalov]

Originally Posted by Mini-Geek

...You could probably speed the search significantly by sieving in advance using a program like srsieve, then giving the sieved file to PFGW and not using the -f100 command. I suspect that this is how Batalov has continued the search into the tens of thousands of digits, which certainly wouldn't be very fast (if possible) with Java.

Exactly. I tried to leave it to spkarra to figure out, but because this doesn't seem to be happenning, forgive me for bluntly spelling this out now:
spkarra, you are doing something for a month (and will continue for another year at this rate) - what I (or anyone else here could) have done in one evening. The plus2 series is now done to n<=35000 (with an additional prime PRP at n=214250) and the minus2 series is done to n<=75000, and all prime PRPs are already posted to OEIS and PRP-list (they are in processing, I guess; the maintainers have a life, too).

What is the take home message here? If anything, it is this: one method is never enough (in your case, brute force), and inventing a wheel is never a good option; instead quickly exploring what other methods exist is a must. Don't take it as an offense, alright? I see that you are trying to learn something here; -- ok, you already learned how to do it (somewhat) in Java, now it's time to move on and learn more. Good luck!