Reserved for MF - Sequence 4788

[henryzz]

What is the highest 2^4*31 has been lost?

[RichD]

For this sequence, I knocked one off here.

[science_man_88]

Originally Posted by henryzz

What is the highest 2^4*31 has been lost?

searching factordb for it through the aliquot sequence selection brings up:

302464450620132002992<21>
36072943892238577277247022778243938144883456<44>
1415767501064859248<19>
3141832894...92<109>
21933224531330162416<20>
1453967358...96<108>
1638782940854073904<19>
4390711203...68<99>
1209528545...12<104>
18412050479184368191100122180112<32>
399880994693565806957517104<27>
3156964483...36<108>
29881985883081475837467776336<29>
5628833728627973643098576<25>
360585660037777060955632<24>
7169123053...64<109>
310797102124039979216<21>
1023816193737241913858384<25>
1417854948980933459921072<25>
1417854948980933459922064<25>

as having a factor of it so looks to be about 109 digits for the highest listed there (maybe a limit to the amount of numbers listed though) so maybe see if the sequences involving the higher ones to see if it escaped ? edit: At least one of the sequences looks to have gotten up to 131 digits from a 109 digit start of sequence value before it dropped it all.

[Drdmitry]

There is a chance. :)

[henryzz]

Now on 2^3*3 which is much weaker. The 3 is squared for now as well.

[science_man_88]

Originally Posted by henryzz

Now on 2^3*3 which is much weaker. The 3 is squared for now as well.

the square is no longer:

Unchecked 10204 114 (show) 6410204042...28<114> = 2^3 · 3 · 300733 · 8881361044...09<107>

[henryzz]

Lost it. Now 2^2*3. Just a case of losing the 3 before it will go down slowly.

[science_man_88]

Originally Posted by henryzz

Lost it. Now 2^2*3. Just a case of losing the 3 before it will go down slowly.

it also involves not getting a 7.

[ryanp]

So I guess I jinxed it earlier.

But I can now say I've stuck with this sequence for ~50% of its life... 10K terms and still going!

[henryzz]

Originally Posted by science_man_88

it also involves not getting a 7.

It is impossible to gain a 7 without losing the 2^2. The same arguments can be used to prove this as for losing a 7.

[Raman]

How about posting all of my opinions over here, rather than in their appropriate threads?

@ Ryan Propper: Have you automated submissions to FactorDB even when you are asleep or outside? Great job!
Factoring a c120 in 2006 would take upto 5 days. In 2016, it is only taking 5 minutes. Or 10 minutes may be? Distributed computing is being going on automatically?
Perhaps you could help out with aliquot sequences of 552, 564, 660, 1512, 1992, 5250, 9120, 11040 besides of 4788 or of 314718.

The open end aliquot sequences below 10000 are
276, 306, 396, 552, 564, 660, 696, 780, 828, 888, 966, 996.
Those given in bold are main open end aliquot sequences.
Those not given in bold are side open end aliquot sequences to the above mentioned main open end aliquot sequences.

Originally Posted by 10metreh

I hope I live to see it reach 10000 lines!

Do you mean aliquot sequence 314718 or aliquot sequence 4788? Anyway both aliquot sequences are past 10000 iteration mark right now.
10metreh is not being active these days. Right now aliquot sequence 314718 is at iteration 16744 and counting. Right now aliquot sequence 4788 is at iteration 10284 and counting.

Is 2 the only way of going down by means of a downdriver. Are there no other ways? What about going down by stable guides?
There are many different drivers (perfect numbers - all only known to be even). But there is only one downdriver!
Are there any drivers for odd numbers? Is that statement equivalent to asking for existence of odd perfect numbers?
Any way that an aliquot sequence parity change will occur only for squares or twice squares. They are the only way to terminate an aliquot sequence. Isn't it?

Originally Posted by unconnected

...and now we have squared 3

Say 9, instead of squared 3!
Sometimes that lines like 2³.3².p where p is a prime number that is being congruent to 1 (mod 4) can decompose in the next iteration into
2.3 driver, the driver which is the most difficult to escape from - 2[sup]6[/sup].127 driver. Some one could pray that this does not happen right now at all!
But, we cannot do anything with it! All is natural! Aliquot sequences is a deterministic algorithm, not a randomized algorithm at all!
The downdriver 2 cannot pick up a 3, the stable guide 2² cannot pick up a 7, the stable guide 2⁴ cannot pick up a 31, the stable guide 2⁶ cannot pick up a 127.
Further more that in the aliquot sequence 4788 iteration 8417, the line factored into 2³.3⁴.p where p is a prime number that is being congruent to 1 (mod 12).
Were that p were congruent to 5 (mod 12), the next iteration would have decayed into the 2.3 driver!
Or if aliquot sequence 4788 iteration 10262 or 10284, the line factored exactly into 2³.3².p where p is a prime number that is being congruent to 5 (mod 12).

There are exactly 6460 iterations difference of offset between aliquot sequence 4788 and aliquot sequence 314718.

It took 4 years (2012 - 2016) to reach from previous summit of this aliquot sequence to the current summit, at present.
Previous trench of this aliquot sequence was at 16 digits, the current trench, at present was at 12 digits, the next trench will be at 8 digits, 4 digits and 0 digits, termination!
By the way, by that arrange the following in increasing or decreasing order of height / altitude / elevation.
Trench - Ridge - Shallow seas - Sea level - Plains - Summit - Peak.
By the way, by that what is the exact difference between all these things? And then note - notice!

Originally Posted by unconnected

Minimum at 16 digits and now it grows with 2^2*7 driver.

2².7 driver is the easiest driver to escape, isn't it? Or is it the 2⁴.31 driver?
Any way that you would need 2².7^2k, k ≥ 1 to escape from the 2².7 driver, and then
that you would need 2⁴.31^2k, k ≥ 1 to escape from the 2⁴.31 driver.

A good exercise for analysis:
Arrange the following drivers in the increasing or decreasing order in the probability of their getting escaped from:
2.3 driver, 2².7 driver, 2⁴.31 driver, 2⁶.127 driver.
How about the 2¹².8191 driver, etc.?

Originally Posted by mshelikoff

It looks like it picked up a 2^2·7 at the 16 digit 1987170707261684 , found the downdriver later, and then picked up another 2^2·7 at 20 digits and this one isn't leaving.

The main downdriver for the aliquot sequence 4788 or 314718 from 200 digits exactly ended at 87 digits, eventhough exactly that it did go down upto 16 digits (right now 12 digits!)
The greatest descent for aliquot sequence 1578 or 56440 or 79640 from 110 digits in the Wolfgang Creyaufmüller's page is being given as exactly at 5 digits, although exactly that the main downdriver did end at 58 digits.
By the way by that the greatest ascent for aliquot sequence 1578 or 56440 or 79640 during that peak was exactly at 111 digits, but not exactly 110 digits. However that the greatest ascent for aliquot sequence 4788 or 314718 during that ridge was at exactly 200 digits - exactly.
How do you consider or handle this?

Originally Posted by axn

Currently @ 7960 with 2^3*3 driver (ouch!). Well, at least, it isn't the 2^3*3*5 driver.

What is the difference between 2³.3 driver and 2³.3.5 driver? Or is even 2³.5 being a driver?
On the other hand, by that do 2³, etc. is not being a driver, but only, let alone, a stable guide.

@ LaurV, what does your D2, D3, etc. mean?
Do they mean the drivers 2.3 driver, 2².7 driver, 2⁴.31 driver, 2⁶.127 driver, 2¹².8191 driver, etc.?

@ Dubslow, what does your 1205Z, 1208Z, 1210Z, etc. mean?
And do they mean the Greenwich Mean Time (GMT) and the Universal Coordinated Time (UTC) respectively?
By the way, by that do note or notice that they are not being equivalent at all, but only, let alone, during in the autumn / fall / winter times - not - not - but only, let alone, during in the summer / spring times!
Universal Coordinated Time is being UTC - not - not - Universal Coordinated Time is being UCT - not - not!
Note - notice. Note - notice.
Autumn - fall. Spring - summer - autumn / fall - winter.

11 posts per page!

Waiting for lengthy post for the past few days!

Are all the computations and entries in the FactorDB are being correct? Or are there any chances for errors?
Mainly a Carmichael number or a pseudoprime number is being marked as a PRP number or SPRP number, if it were actually a composite number, albeit chances for such false positives are being very low?
By the way by that what does albeit mean - although - eventhough?

Originally Posted by Raman

How many resources do you have? You are able to crack a p196 very quickly!

Should have been - or
Must have been - or

How many resources do you have? You are able to crack a c196 very quickly!

By the way by that post delete option has been gone away - that ever which ever a way a way.

Law of big numbers:
→ Every big number does try out to keep up its own same driver or downdriver or stable guide without escaping from.
→ It would be interesting if people could predict how much an aliquot sequence can rise or fall.
→ It would be good if an aliquot sequence could link all the open end aliquot sequences below a certain limit.
→ Aliquot sequences tend to find out a level in range to rise to or to fall to.
→ It would be interesting if people could estimate the probability of a certain aliquot sequence that is being getting terminated.
→ It would be interesting if people could consider the probability of a certain aliquot sequence that is being picking up a driver or a downdriver or a stable guide.

Not willing to edit my post any more!

NFS@Home was not active during the year 2014? Factored only one number, namely 3,766+ it seems so! Thus, may be that it was spending out some time idle or taking a break or factoring Fibonacci numbers or Lucas numbers?
Is it possible to get mail notifications from FactorDB if any progress is being made upon any aliquot sequences that I subscribe to? Oops, not to have my inbox getting inundated! However I would enjoy having my inbox getting flooded after having done to other people the same thing!

My user name: Raman, my nickname: Mr. Tuch, my blurb under my user name: Guess what? caseztuchz! OCD Guy!
Spoiler tag is being the most appropriately used with in the puzzles forum only certainly!

Texas State HPC has reserved that 2,2158M c193 for over six years of time without having it as being getting completed off.
May be that some one else or may be that NFS@Home or @ Ryan Propper could be able to - consider it up - up over!
Good work by @ Paul Zimmermann to finish off that Texas State HPC reserved 7,347+ c188 by using ECM curves running immediately, executing out, finishing off with in that composite number, which would have otherwise got no progress at all - during having been a prime number cofactor!

It would be interesting if people could think about that Euler's Totient / Euler's Phi sequence, but not only, let not alone Sum of Factors / Restricted Divisor Function / Aliquot Sequence, namely - not - not!

Should have been - or
Must have been - or

It is being a good idea to replace all the white colour text font by using attachment tags / spoiler tags / strike through tags.

Originally Posted by Raman

Like India population is following China population. When ever do you think that India's population will overtake China's population?

Any way, by that do
By the way, by that do
On the other hand, by that do
Do you think that this incident will eventually happen up?

Right now aliquot sequence 314718 is at iteration 16744 and counting. Right now aliquot sequence 4788 is at iteration 10284 and counting.

FactorDB was down for me from Monday 12 September 2016 8:30 am IST (Indian Standard Time - GMT +0530) to Monday 12 September 2016 12:00 noon IST (Indian Standard Time - GMT +0530).