[QUOTE=Jeff Gilchrist;239652]My largest equal split to date:

[CODE]947_79_minus1
prp108 factor: 412162206264822345435611530468786989259988341878238149275963902235179375322643647900212611682048142360636743
prp108 factor: 602570462034741653744389923449493192747171483035727809190243541878294594097868404630738514951582650349235721
[/CODE][/QUOTE]

As they say in the UK, Brilliant!

[QUOTE=wblipp;239771]As they say in the UK, Brilliant![/QUOTE]Was the ambiguity deliberate, on the grounds that I at least would appreciate the word play, or was it chance?

I'm hoping for the former but, regardless, it is indeed brilliant.

Paul

[QUOTE=xilman;240100]Was the ambiguity deliberate, [/QUOTE]

Yes.

Last week my wife was reading "Private Patient" by P.D. James and came across Brilliant numbers as a plot device. Fay asks "Do you what Brilliant Numbers are?" William replies "They are numbers with two prime factors of the same length - why do you ask?" Fay "So they are real, not just something the author made up!"

A Brent composite, also one of Hisanori Mishima Cyclotomic Numbers and Pace's p^q-1 with no known factors of 12 or more digits.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Pace aka Zetaflux

[code]
983^79-1
P94: 1000102122253158220136804515506925452640552848715960125028992536708499380888800526693799575059
P119: 29023570765769453849681787520675402409630111311649476322178663467954992292617669855309548046285560789566509795994872589
[/code]

I think this factor qualifies. It is rather small, but the composite was large:

[FONT=Arial Narrow]Input number is Phi(2450,10) (841 digits)
Using B1=11000000, B2=30114149530, polynomial Dickson(12), sigma=2316371584
Step 1 took 812415ms
Step 2 took 131024ms
********** Factor found in step 2: 5240352469572867909569390990706187998335241601
Found probable prime factor of 46 digits: 5240352469572867909569390990706187998335241601
Probable prime cofactor (Phi(2450,10))/5240352469572867909569390990706187998335241601 has 795 digits[/FONT]
[FONT=Arial Narrow] [/FONT]
This was very lucky because this was only the 31-st curve at the 45-digit level. The cofactor is a certified prime (it is the 2nd largest helper for two gratuitous 44104-digit CHG prime proofs which it made possible: the factorization ratio jumped from 25.76% to 27.67% - which is a huge leap for CHG). The last helper is a [FONT=Arial Narrow]prp5018[/FONT] and will require a week of Primo and is already in progress.

The two non-trivial 44104-digit primes that will be proven are
[COLOR=#000000][FONT=verdana][FONT=Arial Narrow] [COLOR=blue]7536*10^44100-7537[/COLOR] and[/FONT][/FONT][/COLOR]
[COLOR=#000000][FONT=verdana][FONT=Arial Narrow] [COLOR=blue]9436*10^44100-9437[/COLOR][/FONT][/FONT][/COLOR]
[COLOR=#000000][FONT=verdana] [/FONT][/COLOR]
[COLOR=#000000][FONT=verdana]--Serge[/FONT][/COLOR]
[COLOR=#000000][FONT=verdana] [/FONT][/COLOR]

Much better!
 

This is from another c155 that I just finished (363270:i1730):[code]prp58 factor: 3471537060073909445732093208261232664488685526359035900511
prp97 factor: 3774567531904111499906361116342583365390634599112560322236069538347385670533260739954094206097627
elapsed time 02:07:34[/code]Much better this time....

[FONT=Arial Narrow](-- cofactor of (7*10^157-27*10^78-7)/9 --)[/FONT]
[FONT=Arial Narrow][URL="http://factordb.com/index.php?id=1100000000033032758"]Input[/URL] number is 24233097500762524111940937072936461494997933612649023856782948900925389038336438079896973830843686732126436211601465120646093455187 (131 digits)[/FONT]
[FONT=Arial Narrow]Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=858476354[/FONT]
[FONT=Arial Narrow]Step 1 took 2633ms[/FONT]
[FONT=Arial Narrow]Step 2 took 1696ms[/FONT]
[FONT=Arial Narrow]********** Factor found in step 2: 147694410877021462565125902371474495258474666885142433199593681[/FONT]
[FONT=Arial Narrow]Found composite factor of 63 digits: 147694410877021462565125902371474495258474666885142433199593681[/FONT]
[FONT=Arial Narrow]Composite cofactor 164075927835484185961638927617606398269462297468570739789185011801827 has 69 digits[/FONT]


That's funny even though not too surprising.
Final split = p31.p32.p33.p38

In a whimsical mood last night, I started 2 million curves at B1=11k on a 70 digit rsa number [SIZE="1"](note to computation nazis: this was also a test of a new feature of YAFU...)[/SIZE]. Three hours later, on curve number 1511916, this popped out:

[CODE]prp35 = 36372793201675991076296101402541399 (curve 378020 stg2 B1=11000 sigma=797060956 thread=2)
[/CODE]

Group order:
[CODE][ <2, 5>, <3, 3>, <5, 1>, <13, 1>, <43, 1>, <89, 2>, <239, 1>, <269, 1>, <1031,
1>, <1877, 1>, <2293, 1>, <6163, 1>, <1081513, 1> ][/CODE]

This was only 448 times slower than siqs would have been :smile:

Nice split from aliquot sequence 84054, iteration 927, c107 cofactor:

[CODE]prp54 factor: 256987839630433114855860600463944635827606033208686423
prp54 factor: 267555805714436556315915777170207798884252871568343457[/CODE]

Pretty large for 1e6 --
[FONT=Arial Narrow]Input number is 5899329538881140541125238042893031867466785687022406886616631619373395333279906132944250638737474559479712543418870762690649 (124 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1978780349
Step 1 took 2492ms
Step 2 took 1560ms
********** Factor found in step 2: 74497034660233574745524000914673751584591971201
Found probable prime factor of 47 digits: 74497034660233574745524000914673751584591971201
Probable prime cofactor 79188783362812095602986433960506228690971306598852634601709885645902479941849 has 77 digits[/FONT]

Got this split via ECM (c127 from Aliquot 330084:i367):[code]a.c127 / 492723851585952114366759131977295316907053319594877:probable:14946374457217282656627092631806933080428720517983578896373851328950907664211:Probable finder: me:Machine_1:v2.0k B1:43000000 sigma: -722316553[/code]I put this in my ECMNET setup while I ran another, "easier", one and caught a p51 * p77 split!