User TJAOI

[tha]

Just for the record, I assume user TJAOI started at bit level 1 and worked up from there to the current level. I also assume that all factors he finds are turned in to the Primenet server, which only records factors not found before. So, basically this is a Double Check factoring effort with the benefit of all exponents in the database being fully factored up to the current level instead of to the lowest found factor.

If anything is different I would like to hear about it.

[VBCurtis]

Originally Posted by tha

Just for the record, I assume user TJAOI started at bit level 1 and worked up from there to the current level. I also assume that all factors he finds are turned in to the Primenet server, which only records factors not found before. So, basically this is a Double Check factoring effort with the benefit of all exponents in the database being fully factored up to the current level instead of to the lowest found factor.

If anything is different I would like to hear about it.

There is no 'bit level 1', because mersenne factors are of the form 2kp+1. One would start at k=1, which means for a 100M exponent the smallest possible factor is 200M; that's 27.xx bits.

This also means that for a search like TJAOI's, the bit level determines how big the largest possible number factored is; one simply cannot find a 30-bit factor for a Operation Billion Digits number!

[TheMawn]

These ranges have not had any P-1 done to my knowledge, with a few exceptions where people take particular interest in a specific exponent. Almost all of the exponent summaries show no record of P-1. It's not nearly as practical to perform a breadth-first P-1 search as it is a TF breadth-first search.

Most of these would have been found with a small dose of P-1 because of their size. As a quick estimate you can go to http://www.mersenne.ca/prob.php and punch in some parameters yourself. Take any Mersenne Number and its factor Q. Find the factors of Q-1. One of them must be the exponent P. Aside from that one, look at the largest remaining factor (include its power). That is the absolute smallest B1 you could have used to find this factor with stage 1 P-1.

For example, for 2^129966737 - 1, the factor Q = 119091404770351998473 and Q - 1 = 2^3×523×6217×35227×129966737.

Doing P-1 on that exponent with B1 = 35227 costs 0.27 GHz-Days. It doesn't seem like much, but take into consideration the fact that we might not have done any P-1 on that exponent until we reached maybe 78 bits. The odds of finding a factor with a B1 that low are about 1 in 500, so we would have ended up going much higher which takes more computing power yet (not to mention all the TF wasted getting the bit level to the appropriate point in the first place.


All in all, we're quite fortunate that someone has dedicated enough effort to a factor search by K instead of by P to find these gems for us.

When we get closer to that range, we will need to decide if we trust that TJAOI found everything below whatever threshold or if we take measures to double-check for factors. Like I said before, we may be able to get an idea of how many factors are still missing and try to estimate how many are left and decide how much firepower it is worth it to spend trying to find them. If the odds of a candidate having a missing factor are even 1 / 1000 it won't be worth it to spend very much effort looking for it.

[tha]

Originally Posted by VBCurtis

There is no 'bit level 1', because mersenne factors are of the form 2kp+1. One would start at k=1, which means for a 100M exponent the smallest possible factor is 200M; that's 27.xx bits.

User TJAOI checks in factors for very low exponents as well, I found a 1M exponent checked in today.

[owftheevil]

I've found two factors, 65 and 67 bits (if I remember correctly) by p-1 on numbers supposedly tfd to 74 bits. Both had been done in 2010 at the level where the factors were missed.

[TheMawn]

Originally Posted by tha

User TJAOI checks in factors for very low exponents as well, I found a 1M exponent checked in today.

Instead of trying a bunch of factors for a specific candidate, he is checking factors (2*k*p + 1) with specific k and seeing if they are factors for a specific exponent.

For example, start with k = 1 and test every single p by seeing if 2kp+1 is prime itself divides 2^p - 1.

Then, go to k = 2.


There's no reason for him to not find factors for lower exponents. It's just less likely.

[Anonuser]

Originally Posted by bloodIce

What is the approximate number of the newly factored numbers by TJAOI? Several hundreds may be?

This number is probably bigger than 200. I have found another 88 exponents. Therefore, there should be at least 60+51+88=199 exponents that have been cleared by TJAOI.

238521893 243069601 246439639 248744597 272031449 272794003 272941007 283522271 299392693 324447163 325824481
329918063 333745177 345732643 350682499 363655373 382419637 387629743 388040603 392987779 395278649 399598349
404924413 409550381 415560947 420625693 423150461 427273709 428341763 451320017 456683473 466851653 482424673
495980827 507102601 512268683 530871521 533148851 534244129 540156979 548147021 548330617 565154141 578286563
579301693 580837519 586859353 603669383 617198287 622548529 643358173 649232917 654311477 689741839 704410933
708359671 716352467 717926719 741946957 748118741 752159647 756776413 758241097 762466739 773023793 775808233
786465419 803141509 804428809 813000103 820197583 842145929 850352507 857116471 858799187 860977333 861415363
862069937 865151479 883622309 902980087 904083407 925918793 929794609 931376821 936759839 973750237 981847247

[petrw1]

Just a thought but those who have direct access to the database could quite easily write a query to find all recently found factors that were missed earlier.
TJAOI might not be the only one who has found some.....though (s)he apparently found the most.

Then an analysis of what was missed:
--- What bit ranges (maybe 55-56 only???)
--- What exponent ranges (seems to be all)
--- What time period the ranges with the missing exponents were being worked on
--- What version of Software was being used then
it could be determined which groups of exponents most likely needs to be rechecked.

OR....we can just wait until TJAOI find them all himself :)

[S485122]

Originally Posted by petrw1

Then an analysis of what was missed:
--- What bit ranges (maybe 55-56 only???)

If I remember well, Prime95 by default stops at the first factor found. but within a bit range potential factors are checked by classes not sequentially. This means that a smaller factor found by TJAOI within the same bit range does not automatically imply a missed factor by a previous run.

Jacob

[VBCurtis]

Originally Posted by S485122

If I remember well, Prime95 by default stops at the first factor found. but within a bit range potential factors are checked by classes not sequentially. This means that a smaller factor found by TJAOI within the same bit range does not automatically imply a missed factor by a previous run.

Jacob

However, the ~200 mentioned in this thread are numbers that were not previously factored- click on a link or 5 to see what I mean.

[TheMawn]

A lot of the exponents supposedly factored to 65 or 66 actually only have a record starting at 64 and some at 63.