mersenneforum.org Reserved for MF - Sequence 4788
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 2012-05-13, 23:45 #1948 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2012-05-14, 02:51 #1949 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2012-05-14, 04:20 #1950 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
2012-05-14, 05:20   #1951
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2×1,061 Posts

Quote:
 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:
Code:
 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):
Attached Thumbnails

2012-05-14, 06:22   #1952
LaurV
Romulan Interpreter

Jun 2011
Thailand

52×7×53 Posts

Quote:
 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)

Last fiddled with by LaurV on 2012-05-14 at 06:24

2012-05-14, 06:41   #1953
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

160658 Posts

Quote:
 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: Code:  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?
Quote:
 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).

Last fiddled with by Dubslow on 2012-05-14 at 07:13 Reason: gotta love the smileys

2012-05-14, 09:16   #1954
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

5×172 Posts

Quote:
 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.

2012-05-14, 09:30   #1955
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3×29×83 Posts
Double Post

Quote:
 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;
Code:
sum: have completed work to t38.16
That means 1224@3M. I'm bowing out here to tackle 3366, as previously noted.

Last fiddled with by Dubslow on 2012-05-14 at 09:49 Reason: Adding post 2

 2012-05-14, 16:33 #1956 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 32×17×61 Posts 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).
 2012-05-15, 10:14 #1957 rajula     "Tapio Rajala" Feb 2010 Finland 32·5·7 Posts 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).
 2012-06-10, 15:08 #1958 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 3×419 Posts 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 Last fiddled with by Raman on 2012-06-10 at 16:08

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