fond of a factor? Urn yourself to become remains

[LaurV]

Good catch, but that was not the point. Who is going to test them? Are you?

[axn]

Originally Posted by LaurV

Good catch, but that was not the point. Who is going to test them? Are you?

Worse still. You're better off doing ecm on these low numbers. And GIMPS has already done a lot of ecm on them. So there is very little possibility of TF succeeding at these low numbers.

[LaurV]

Originally Posted by axn

And GIMPS has already done a lot of ecm on them

Pls note we were talking about numbers with some factors known already. There is not "so much" ECM done for them, all the forces are/were concentrated on numbers with no known factors (like M1061 and its bigger brothers), for which I already specified the futility of trial factoring. The lots of ECM done for them is an additional reason why TF is futile here, as you said.

But for numbers with already known factors, not so many people bothered to find additional factors, as the compositeness is "already clear". Usually the TF process stopped when a factor was found (we are talking "old times", the "Age of Legends" of GIMPS), and since then, no one bothered anymore with the respective exponents. There could still be place to dig, for curiosity, or other reasons (see the Axon's thread). Here, if someone would be interested in programming/testing/understanding how things work, etc, as OP said, or be interested in that small factors effectively, he could try to play. I believe any of us started long ago with trying to write TF programs for small factors and small exponents, these are the simplest things to program, and you still can learn a lot from it. (not you, axn,:P, I mean generally)

[LaurV]

Well, forget about the 2^39, respectively 2^48, which I mentioned before. It seems as ALL exponents below 7.06M were TF-ed to 2^60, regardless of the fact that they had or they had not, any known factor. At least this can be seen from some older threads here around, where people also talked this subject 6-7 years ago.

So, there should be no missing factor below 2^60 for expos below 7.06M. You have to look at higher bitlevels, and/or higher expos to have any chance to get a new factor for the low-range expos.

[zchacrea]

Thanks for all the information!

I have a hypothesis that isn't panning out well right now, so I've been practicing mathematical coding and watching the numbers play out. It is remarkably easy to code the TF method. Efficient? No. Effective, yes. Plus I enjoyed watching my readout as my program ran.

I can completely understand not listing the 100 digit primes to save space. It seems odd to me that some factors aren't explicitly written though. Is that a local tradition? Or just a more concise way of writing factors that my limited scholastic experience never reached?

Is there a "complete" list of factors of Mersenne Numbers somewhere out there?
GIMPS (understandably) only pays attention to the p = prime exponents.

[wblipp]

Originally Posted by zchacrea

Is there a "complete" list of factors of Mersenne Numbers somewhere out there? GIMPS (understandably) only pays attention to the p = prime exponents.

Will Edgington's Mersenne Page

Note that algebraic factors are not repeated, so you will need to factor the exponent and look up the factorization of algebraic factors separately.

[cheesehead]

Originally Posted by zchacrea

I can completely understand not listing the 100 digit primes to save space. It seems odd to me that some factors aren't explicitly written though.

The only deliberately unwritten factor is the largest factor of a completely-factored number. That factor's value can easily be computed by dividing the number by the product of all the other factors.

Since you can understand not listing a 100-digit prime to save space, isn't it just as easy to understand not listing a 99-digit, 98-digit, 97-digit, or any other length final (prime) factor for the same reason?

Is that a local tradition?

Local to mathematics :-)

Or just a more concise way of writing factors that my limited scholastic experience never reached?

Keep in mind that the tradition was established many years ago (as were almost all mathematical traditions) when factors were more commonly being written by hand.

[markr]

On mersenne.org, is there a simple way to tell which mersenne numbers are completely factored? All I can work out is it ought to be the ones on the known factors page that aren't on the ECM progress page.

[cheesehead]

Originally Posted by markr

On mersenne.org, is there a simple way to tell which mersenne numbers are completely factored?

AFAIK the only way is to start by looking at the "Factoring Limits" report, and note which prime exponents are NOT listed there. Mersenne numbers with prime exponents that are NOT listed in the "Factoring Limits" report are either prime or have been completely factored.

Then, one has to compare the list of exponents NOT in the "Factoring Limits" report with the list of exponents that ARE on the "Known Primes" list, and subtract the latter from the former to get the list of completely-factored numbers.

Oh ... you specified "simple" ...

No.

All I can work out is it ought to be the ones on the known factors page that aren't on the ECM progress page.

... but that would presume that the ECM progress page lists all not-yet-factored ones. It doesn't; it lists only exponents for which there has been at least one ECM effort.

[markr]

Originally Posted by cheesehead

AFAIK the only way is to start by looking at the "Factoring Limits" report, and note which prime exponents are NOT listed there. Mersenne numbers with prime exponents that are NOT listed in the "Factoring Limits" report are either prime or have been completely factored.

?? I thought an exponent was removed from the factoring limits report when even one factor was found. That report is the starting-point when getting one's choice of LMH-type work.

... but that would presume that the ECM progress page lists all not-yet-factored ones. It doesn't; it lists only exponents for which there has been at least one ECM effort.

Thanks for that information.

Given there's no "completely-factored" flag in the mersenne.org reports (AFAIK) I think we'll have to count comparing two lists as simple enough.

[firejuggler]

M54844001 has a factor: 1588991208980582426527
k= 3^2 * 13 * 23 * 5383301093 would have been very hard to find with P-1