What does "Fact bits" mean?

2003-12-30, 17:48

Hello,

I’ve a question. I was loading today my page with the personal stats, but I can’t understand what the field “fact bits” mean. It gives 67 for one exponent and 57 for another that is in the pipe to be processed next. What does that mean?

Thanks and Happy New Year!

nfortino · 2003-12-30, 17:57

Fact bits is how far the number you are testing has been trial factored. The first one has been trial factored up to 2^67, and the second has been trial factored up to 2^57. After you finish the first, you will trial factor the second up to 2^67, and then (assuming no factor is found) do a Lucas-Lehmer test for primality.

2003-12-30, 20:16

Thanks! Is this that stage one and stage Two thing before the LL is run?

nfortino · 2003-12-30, 20:42

Quote:

Originally posted by Unregistered
Thanks! Is this that stage one and stage Two thing before the LL is run?

No, that's a kind of factoring called p-1 factoring. Trial Factoring tests every possible divisor up to 2^67 for current exponents. P-1 factoring can find an arbitrarily large factor, but only if it has a special form. This is explained in more detail here.

dsouza123 · 2003-12-30, 20:44

The possible steps for doing a LL are:

- Trial Factor to a limit based on the size of the exponent.

- P-1 Factor to a some limit, it has two stages. The second stage isn't done if not enough memory is allocated.

- LL test.

If a mersenne number has already been trial factored to the program limit, the TF test is skipped.

If it has already been P-1 factored that stage will be skipped, tipically this will happen for double checks.

Finally the LL (Lucas-Lehmer) test is run. A double check is just a second LL on a previously tested LL for verification.

There is a setting to skip trial factoring.

2003-12-30, 17:48	#1
Unregistered 3033₈ Posts	What does "Fact bits" mean? Hello, I’ve a question. I was loading today my page with the personal stats, but I can’t understand what the field “fact bits” mean. It gives 67 for one exponent and 57 for another that is in the pipe to be processed next. What does that mean? Thanks and Happy New Year!

2003-12-30, 20:44	#5
dsouza123 Sep 2002 296₁₆ Posts	The possible steps for doing a LL are: - Trial Factor to a limit based on the size of the exponent. - P-1 Factor to a some limit, it has two stages. The second stage isn't done if not enough memory is allocated. - LL test. If a mersenne number has already been trial factored to the program limit, the TF test is skipped. If it has already been P-1 factored that stage will be skipped, tipically this will happen for double checks. Finally the LL (Lucas-Lehmer) test is run. A double check is just a second LL on a previously tested LL for verification. There is a setting to skip trial factoring. Last fiddled with by S485122 on 2007-03-07 at 11:43 Reason: corrections

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2003-12-30, 17:57	#2
nfortino Nov 2003 3×5×11 Posts	Fact bits is how far the number you are testing has been trial factored. The first one has been trial factored up to 2^67, and the second has been trial factored up to 2^57. After you finish the first, you will trial factor the second up to 2^67, and then (assuming no factor is found) do a Lucas-Lehmer test for primality.

2003-12-30, 20:16	#3
Unregistered 5·1,567 Posts	Thanks! Is this that stage one and stage Two thing before the LL is run?