Gratuitous factors thread - Page 29

fivemack · 2012-05-13, 23:10

Quote:

Originally Posted by fivemack

Will try a C160 with the larger large primes and see if I can find the crossover point.

A C159 with Murphy 1.733 sieved with 31LP in almost exactly the same time as a similar-sized C159 with Murphy 2.183 and 30LP. So I think I prefer 31LP at that level too.

Batalov · 2012-06-02, 05:07

A few gratuitous and patently silly factors (non-algebraic):

82*2^17681-81 is a prp and divides MM17681
112*2^10457-111 is a prp and divides MM10457
10*2^863-9 divides MM863
1968*2^229-1967 divides MM229
1944*2^271-1943 divides MM271

fivemack · 2012-06-07, 06:52

(2232.1045)

Code:

prp75 factor: 147862046859949267414841968169633849223604114880934142142092204556044870187
prp75 factor: 473607548107446907344419401894968758748844789613352095008694042735830826261

Batalov · 2012-06-07, 16:59

Lucas1249 c262 = p115 * p147

Code:

p115 = 1230907246701748850213178915950086177557919307463961418238191238338563780421891858424331033928188919064775254538919
p147 = 861662799748056902967441789531902541845512917066647559276041990818216830987090087949122773698681932527206937859817129749788517846169149201190846679

B+D

(EDIT: the reason for it to be mildly interesting is that the previously known largest penultimate factors were p98 in Fibonacci and a recent p95 in Lucas factorizations.)

bdodson · 2012-06-08, 15:17

Quote:

Originally Posted by Batalov

Lucas1249 c262 = p115 * p147
...
B+D

(EDIT: the reason for it to be mildly interesting is that the previously known largest penultimate factors were p98 in Fibonacci and a recent p95 in Lucas factorizations.)

A second point of interest, the matrix was 14.59M^2 with a Serge
binary using zlib and aiming for density 100. This took c. 19 node-days
on our cluster, using six threads on a single node with 2 8-core cpus.

This was our first test-case for msieve-mpi; for which a "stock"
compile (no zlib or density) gave a 16.5M^2 matrix. The timing for
4 nodes, 16 cores/node is just in

Code:

Thu Jun  7 18:36:35 2012  initialized process (0,0) of 8 x 8 grid
Thu Jun  7 18:39:08 2012  matrix starts at (0, 0)
Thu Jun  7 18:39:09 2012  matrix is 2064182 x 1749228 (154.4 MB) with weight 55236916 (31.58/col)
Thu Jun  7 18:39:09 2012  sparse part has weight 22970121 (13.13/col)
Thu Jun  7 18:39:09 2012  saving the first 48 matrix rows for later
Thu Jun  7 18:39:09 2012  matrix includes 64 packed rows
Thu Jun  7 18:39:17 2012  matrix is 2064134 x 1749228 (132.4 MB) with weight 25403865 (14.52/col)
Thu Jun  7 18:39:17 2012  sparse part has weight 17224508 ( 9.85/col)
Thu Jun  7 18:39:17 2012  using block size 262144 for processor cache size 10240 kB
Thu Jun  7 18:39:18 2012  commencing Lanczos iteration
Thu Jun  7 18:39:18 2012  memory use: 207.8 MB
Thu Jun  7 18:39:38 2012  linear algebra at 0.0%, ETA 57h19m

which looks like a 50% savings in node-days.

Bruce (for Batalov+Dodson, with thanks to Jason, Greg and Lehigh's HPC group)

Dubslow · 2012-06-27, 01:03

Slightly nicer split than fivemack's above:
http://factordb.com/index.php?id=1100000000520244816

Code:

PRP46 = 1620979858139715654164015438978958404260540673
PRP46 = 4376012889530283193868474423962504495931269487

854628.2079

Dubslow · 2012-06-28, 19:49

http://factordb.com/index.php?id=1100000000520518828

Code:

starting SIQS on c92: 34164189955789536053590089105629252537838430612716698097997774549446989508175466797330208963
...
PRP46 = 5567633869391458324478744885324975214045868961
PRP46 = 6136213471868199135213045365634727120644813283

Ratio is 1.102.

A544608.1138

Batalov · 2012-06-28, 21:53

There exists a couple of p76 . p76 splits in aliquot sequences.
One is in 9120:i869
Another is in 3906:i1848 ...

If you are interested in the ratio (and at least 45 digits), then there are some ratios like 1.00054 (11820:i1061), 1.00093(277344:i1508), 1.00086 (405420:i1101)...

There's also a 32090656388032554397472480978461 * 32091162549556209617436569529601 split (ratio 1.00002), if you look at smaller numbers.

There's a p108 . p108 nice split outside of aliquot sequences.

LaurV · 2012-06-29, 03:05

I had two p67 split in one of my sequences, I forgot which one, but I remember I was boasting on the forum about it. That is the max brilliant I ever split in... real life (i.e. not counting deliberately-manufactured brilliant numbers some people are posting here from time to time and ask for help to factor them).

ET_ · 2012-07-03, 14:33

I don't know if this is the right place to tell...

Code:

Trial-factoring M1951951 in [2^1, 2^41-1]
M1951951 has a factor: 54562292909897 - Program: L5.0x
M1951951 has a factor: 81981943 - Program: L5.0x
M1951951 has a factor: 1511251214927 - Program: L5.0x
M1951951 has 3 factors in [2^1, 2^41-1].

54562292909897 was not found. I added it to mersenne-aries site; is there a way to show it to the GIMPS archive?

I'm mailing George as well.

Luigi

henryzz · 2012-07-03, 16:21

Quote:

Originally Posted by ET_

I don't know if this is the right place to tell...

Code:

Trial-factoring M1951951 in [2^1, 2^41-1]
M1951951 has a factor: 54562292909897 - Program: L5.0x
M1951951 has a factor: 81981943 - Program: L5.0x
M1951951 has a factor: 1511251214927 - Program: L5.0x
M1951951 has 3 factors in [2^1, 2^41-1].

54562292909897 was not found. I added it to mersenne-aries site; is there a way to show it to the GIMPS archive?

I'm mailing George as well.

Luigi

Submitting it via the manual pages should work I believe.

2012-06-02, 05:07	#310
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	A few gratuitous and patently silly factors (non-algebraic): 822^17681-81 is a prp and divides MM17681 1122^10457-111 is a prp and divides MM10457 102^863-9 divides MM863 19682^229-1967 divides MM229 19442^271-1943 divides MM271 Last fiddled with by Batalov on 2012-06-02 at 07:24*

2012-06-07, 06:52	#311
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²·131 Posts	Quite nice split (2232.1045) Code: prp75 factor: 147862046859949267414841968169633849223604114880934142142092204556044870187 prp75 factor: 473607548107446907344419401894968758748844789613352095008694042735830826261

2012-06-07, 16:59	#312
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	Lucas1249 c262 = p115 * p147 Code: p115 = 1230907246701748850213178915950086177557919307463961418238191238338563780421891858424331033928188919064775254538919 p147 = 861662799748056902967441789531902541845512917066647559276041990818216830987090087949122773698681932527206937859817129749788517846169149201190846679 B+D (EDIT: the reason for it to be mildly interesting is that the previously known largest penultimate factors were p98 in Fibonacci and a recent p95 in Lucas factorizations.) Last fiddled with by Batalov on 2012-06-07 at 18:55

2012-06-27, 01:03	#314
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 1110000110101₂ Posts	Slightly nicer split than fivemack's above: http://factordb.com/index.php?id=1100000000520244816 Code: PRP46 = 1620979858139715654164015438978958404260540673 PRP46 = 4376012889530283193868474423962504495931269487 854628.2079 Last fiddled with by Dubslow on 2012-06-27 at 01:04

2012-06-28, 19:49	#315
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3×29×83 Posts	Amazing split http://factordb.com/index.php?id=1100000000520518828 Code: starting SIQS on c92: 34164189955789536053590089105629252537838430612716698097997774549446989508175466797330208963 ... PRP46 = 5567633869391458324478744885324975214045868961 PRP46 = 6136213471868199135213045365634727120644813283 Ratio is 1.102. A544608.1138 Last fiddled with by Dubslow on 2012-06-28 at 19:55

2012-06-28, 21:53	#316
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22405₈ Posts	There exists a couple of p76 . p76 splits in aliquot sequences. One is in 9120:i869 Another is in 3906:i1848 ... If you are interested in the ratio (and at least 45 digits), then there are some ratios like 1.00054 (11820:i1061), 1.00093(277344:i1508), 1.00086 (405420:i1101)... There's also a 32090656388032554397472480978461 * 32091162549556209617436569529601 split (ratio 1.00002), if you look at smaller numbers. There's a p108 . p108 nice split outside of aliquot sequences.

2012-06-29, 03:05	#317
LaurV Romulan Interpreter Jun 2011 Thailand 258B₁₆ Posts	I had two p67 split in one of my sequences, I forgot which one, but I remember I was boasting on the forum about it. That is the max brilliant I ever split in... real life (i.e. not counting deliberately-manufactured brilliant numbers some people are posting here from time to time and ask for help to factor them).

2012-07-03, 14:33	#318
ET_ Banned "Luigi" Aug 2002 Team Italia 1001011001111₂ Posts	I don't know if this is the right place to tell... Code: Trial-factoring M1951951 in [2^1, 2^41-1] M1951951 has a factor: 54562292909897 - Program: L5.0x M1951951 has a factor: 81981943 - Program: L5.0x M1951951 has a factor: 1511251214927 - Program: L5.0x M1951951 has 3 factors in [2^1, 2^41-1]. 54562292909897 was not found. I added it to mersenne-aries site; is there a way to show it to the GIMPS archive? I'm mailing George as well. Luigi

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