What is Trial Factoring?
 

I recently installed Prime95 on a computer and it started trial factoring instead of LL. Why is this? What is trial factoring exactly?

[URL]http://mersenne.org/various/math.php[/URL]

It may be that you have an older computer. This could cause it to do
TF. Or, the number that you received still needed some TF testing.

Or you decided that your PC would only run for a few hours a day.

Luigi-

As you can determine by studying the link which Batalov provides, the LL test is costly in terms of computer time spent and is only performed on those Mersenne numbers for which no factor has been found and which therefore could still be prime. Trial Factoring and P-1 Factoring are both used to eliminate candidates by finding factors, and only those Mersenne numbers which pass these stages without turning up a factor are given on to the expensive LL testing stage which finally determines their compositeness or primality.

If you especially want to do LL testing or any other particular work type, try setting your default work type by logging into PrimeNet and going to [URL]http://www.mersenne.org/worktype/[/URL].

An analogous way to think of it is to think of a given Mersenne number as a criminal defendant. Either the defendant is guilty (the number is not prime) or the defendant is innocent (the number is prime).

Just as a criminal defendant can enter an early plea of guilty and avoid a trial, we perform trial factoring on a Mersenne number (offering it a plea bargain, perhaps?). The number either easily gives up a factor, as the guilty criminal gives up her plea, or the number clams up. In the latter case, just how we would proceed with a nontalking defendant, we have to "try" the Mersenne number. We do this by means of the LL test. Thankfully, an LL test is not subject to elected officials, media scrutiny, celebrity, etc. But I digress. The LL test, like a criminal trial, gives us a definitive answer at the end: prime/not guilty or not prime/guilty. But it costs a whole heap more in time and resources than if we just were to get a guilty plea/factor during the TF stage.

Clear as mud, eh? :smile: