Factoring Fermat Numbers

[philmoore]

It is extremely unlikely, but not impossible, that you would ever find two factors at once, but you could easily do a primality test to see if your factor is prime or not. In most cases, the size of your factor would be an important clue. Suppose you were running curves with B1=250,000 on Fermat numbers and found a factor of 30 digits or so. For this factor to be composite, it would have to have a prime factor of <= 15 digits that would have already been discovered. On the other hand, suppose you turned up a factor of 60 or so digits. The chance of two 30 digit factors showing up on the same curve is about 1 in 700^2, or 1 in 490,000, not very great. On the other hand, the chance of a 60 digit factor showing up with B1=250,000 is much, much smaller than this, so the suspicion that you had found two factors at once would probably turn out to be true.

[clowns789]

Here's a link to ADingOD FreeRAM.

It speeds up GIMPS about 25%.

You should just keep hitting "Optimize" until the numbers don't change anymore.

http://www.padring.com/go.php?http://ading.hypermart.net/freeram.zip

[PageFault]

We have had members who found doubles in P-1. The client tends to concatenate the results and the result then has too many bits for the cleared exponents page. George then intervenes.

[Mr. P-1]

Originally Posted by PageFault

We have had members who found doubles in P-1. The client tends to concatenate the results and the result then has too many bits for the cleared exponents page. George then intervenes.

This has happened to me twice. If there are two factors prime factors within the search space, the result of the P-1 calculation will be their product. The client does not test results for primality nor attempts to factor them, nor apparently does the server. However George does with any unfeasibly large factors turned in.

As you have observed, the cleared exponents page does not show large factors correctly. The last composite I turned in was only shown to 100 bits, however a 102 bit prime factor was shown correctly. I don't know what the limit is.

Regards

Daran