Reserved for MF - Sequence 4788

[Dubslow]

Seems no one's doing it. I'll do it, shouldn't take more than an hour or two.

[Dubslow]

Line 4824
Line 4825

Unfortunately, "bc - An arbitrary precision calculator language" returned 0 for (large-small)/small, and I have not the slightest clue to pari/gp. (Anybody who cares can surely figure it out on their own.)

Edit: 4826 is pretty close as well, though not quite as close as the first two.

[Dubslow]

I'll have NFS on the C122 (line 4826) done in 12-13 hours.

[schickel]

Originally Posted by Dubslow

So much happened while I was gone! So close! 33 digits... dang. How easy is it to escape 2^4*31?

I think it's probably the easiest of the perfect number drivers. 2*3 is the worst, since the line has to essentially factor as 2 * 3^2 * p, 2^2 * 7 is a little easier, since you can have, essentially, 2 other factors for the eascape, and 2^6 * 127 is very hard, since the 127 doesn't get raised above 1 very often.

Clifford records the highest escape from 2^4 * 31 as 129 digits in 5778. I escaped it at 113 digits in 48462 via this factorization:

 1236 .  c113 = 2^4 * 31^2 * 6188785238747719 * 230402350198068564832070130054678954206970878230960200048690011877198238894335419716602085901
 1237 .  c113 = 2^5 * 31 * 71 * 746231 * 144030777132837510217987539096343417010500889513 * 2902096090182134830390738125010054022390760487434126181

I guess we can keep plugging away on 4788 while there's still hope. If we want another community project, we can pick up 3366 when Dubslow runs out of steam. (Interesting because it is >165 digits with no driver presently....)

PS. For those of you that haven't seen it yet, here's the graph (2 troughs at 33 and 35 digits):

[LaurV]

Originally Posted by schickel

Clifford records the highest escape from 2^4 * 31 as 129 digits in 5778. I escaped it at 113 digits in 48462

Wow! that means I can make history with 95280 (a merge from my initial reservation of 6^7=279936) which is now a C132=D4*3*7*C128, and maybe with 189140 too, but this is still small C122=D4*...*C112.

Or should I pray for 618480 (1856: C140=2^4*3^3*...*C134) to get a 31??
(and then pray harder to lose it in few terms? hehe)

[Dubslow]

Originally Posted by schickel

I think it's probably the easiest of the perfect number drivers. 2*3 is the worst, since the line has to essentially factor as 2 * 3^2 * p, 2^2 * 7 is a little easier, since you can have, essentially, 2 other factors for the eascape, and 2^6 * 127 is very hard, since the 127 doesn't get raised above 1 very often.

Clifford records the highest escape from 2^4 * 31 as 129 digits in 5778. I escaped it at 113 digits in 48462 via this factorization:

 1236 .  c113 = 2^4 * 31^2 * 6188785238747719 * 230402350198068564832070130054678954206970878230960200048690011877198238894335419716602085901
 1237 .  c113 = 2^5 * 31 * 71 * 746231 * 144030777132837510217987539096343417010500889513 * 2902096090182134830390738125010054022390760487434126181

So you're saying we basically need 31^2 and hope the rest isn't smooth?

Originally Posted by schickel

I guess we can keep plugging away on 4788 while there's still hope. If we want another community project, we can pick up 3366 when Dubslow runs out of steam. (Interesting because it is >165 digits with no driver presently....)

I still see the C145 that was being finished off by CC... (though if he emailed me in the last few days I missed it. I suppose I'll check.) Edit: Wow... it really got piled in. Somehow I missed his email from two weeks ago. I'll get right on it (after the C122 finishes, for which I'm using all four cores).

[R. Gerbicz]

Originally Posted by Dubslow

So you're saying we basically need 31^2 and hope the rest isn't smooth?

Escaping from 2^4*31 isn't very hard, see the elf file for 5778. Between line 390-973 we have 2^4*31^e, for e>0. And for 21 times e=2, for one time e=3 and for the rest e=1. So escaping it is easy but on the next line we see again 2^4*31. I would say it is hard to kill the 31 as a factor in 2^4*31.

[Dubslow]

Originally Posted by R. Gerbicz

Escaping from 2^4*31 isn't very hard, see the elf file for 5778. Between line 390-973 we have 2^4*31^e, for e>0. And for 21 times e=2, for one time e=3 and for the rest e=1. So escaping it is easy but on the next line we see again 2^4*31. I would say it is hard to kill the 31 as a factor in 2^4*31.

Looks like 972 and 804 were potential escapes, but the rest of them were definitely pretty darn smooth. (If my understanding of schickel is accurate.)



Edit: I have the last post, so I'll use it. That C122 split as a P59*P63, a pretty nice split. In the meantime, the C124 is almost ready for NFS;

sum: have completed work to t38.16

That means 1224@3M. I'm bowing out here to tackle 3366, as previously noted.

[Batalov]

From the tail of sequence 4788, it appears that 31 gets raised to the square only in 1/(2*31) iterations. (Not 1/31 that one would expect from a random process.)

From the same tail, the average gain in every 62 iterations is 10.7 digits (1.49x per iteration).

[rajula]

I advanced the sequence by a couple of iterations. I will not run NFS on the current c124 @ i4841, if it comes to that (so far I have run ECM 800@1M + 300@3M).

[Raman]

What happened to the aliquot.de page? It has not been updated since the April 1 day at all?

Does not contain information regarding the advance for the 4788 (aka 314718) sequence more than 2000 lines; nor the merge of the 345324 sequence (maybe this was being the last one as of now? 9230 open end sequences being remaining below 1000000?)

Mr. Creyaufmüller been on over a long vacation, or otherwise being suffering from a major illness, sorry?

I see that Mr. Clavier's page as well as has got no information relative to the advance for this 4788 sequence, nor since the 9282 sequence downdriver capture event at all, but this is not being worth mentioning at all; since this is being relatively a new incident.

Can the condition be given to escape (to break away) off from the 2⁴*31 driver, to be needed as such?
(31 being raised to the higher even powers is being very rarer enough, though)

Iteration line factoring into The next subsequent line mutates into
2⁴*31²*(1 mod 4 prime) 2*31
2⁴*31²*(3 mod 8 prime) 2²*31
2⁴*31²*(7 mod 16 prime) 2³*31
2⁴*31²*(15 mod 32 prime) 2^>4*31
2⁴*31²*(1 mod 4 prime)*(1 mod 4 prime) 2²*31
2⁴*31²*(1 mod 4 prime)*(3 mod 8 prime) 2³*31
2⁴*31²*(1 mod 4 prime)*(7 mod 16 prime) 2^>4*31
2⁴*31²*(3 mod 8 prime)*(3 mod 8 prime) 2^>4*31
2⁴*31²*(1 mod 4 prime)*(1 mod 4 prime)*(1 mod 4 prime) 2³*31
2⁴*31²*(1 mod 4 prime)*(1 mod 4 prime)*(3 mod 8 prime) 2^>4*31
2⁴*31²*(1 mod 4 prime)*(1 mod 4 prime)*(1 mod 4 prime)*(1 mod 4 prime) 2^>4*31


Even the perfect square factoring or otherwise twice perfect square line is being very highly rare enough that they mutate into an odd number, leading furthermore into very rapid terminating finishes off, away