...but 110 and 112 are the next terms in that sequence. (111 is not a term.)

[FONT=Arial Narrow]Input number is (2+110!)/446 (176 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=664425596
Step 1 took 33854ms
Step 2 took 13759ms
********** Factor found in step 2: 144476918413758184246036836336545025029
Found probable prime factor of 39 digits: 144476918413758184246036836336545025029
Probable prime cofactor ((2+110!)/446)/144476918413758184246036836336545025029 has 138 digits
[/FONT]
[FONT=Arial Narrow]Input number is (2+112!)/136201485670024552186709402 (157 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4290019845
Step 1 took 29010ms
Step 2 took 12301ms
********** Factor found in step 2: 726769575140304566725008000891278612413397880755143
Found probable prime factor of 51 digits: 726769575140304566725008000891278612413397880755143
Probable prime cofactor ((2+112!)/136201485670024552186709402)/726769575140304566725008000891278612413397880755143 has 106 digits
[/FONT]

From aliquot 2340.647:

[code]
C145 =
P48 113417786193133422933533706449636154525514192501*
P49 5623477019926372416647126509445388324954804307727*
P50 13081614163353246775631040196075034249716081205837
[/code]

the P49 was found after about 1600 curves at 3e7, then trivial gnfs for the rest, but it's quite a nice split

From Brent's first holes:

21[SUP]167[/SUP]-1 c207 = p101 x p106

p101 = 20231878724432159106473151940489466149676377569946589675188861313754293570228700650486980343491462439
p106 = 7446031435458004141923577009324871384387277476816498485650562324308647434520507573854037042870112336785089

Method: snfs
Applications: msieve, ggnfs

Many thanks to the authors of these fine applications, to those who laid the theoretical groundwork, and Jeff Gilchrist's excellent tutorial!

Cheers,

Jonathan

Just one of the 350+ P-1 factorizations of the Phi[SUB]n[/SUB](10) without previously known factors:

[CODE]worktodo.txt:
Pminus1=1,10,47227,-1,100000,5000000,"99999999999999999999999999999999999999999999999999999999999999999999999999999999999,11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"
# this is Phi(47227,10)

results.txt:
P-1 found a factor in stage #2, B1=100000, B2=5000000.
10^47227-1 has a factor: 4300229487110655841936172618822201263732668857454598973

# that's 55 digits, and it is composite of course:
# c55 = 78180620476258187 * 3036651139346277721 * 18113301596410660399
# each of them is 2*[I]k[/I]*47227+1[/CODE]

Just a curio. (A triple hit. There were some double hits, as well.)

pre-factorisation gratuity
 

From a C150 of no particular interest:

[code]
Sun Apr 10 19:52:41 2011 polynomial selection complete
Sun Apr 10 19:52:41 2011 R0: -116614098249584146061788052309
Sun Apr 10 19:52:41 2011 R1: 71661578984407507
Sun Apr 10 19:52:41 2011 A0: -3978426728053218287980902072208511006400
Sun Apr 10 19:52:41 2011 A1: 3469871699204920695536279333106656
Sun Apr 10 19:52:41 2011 A2: 407853425618048899990994348
Sun Apr 10 19:52:41 2011 A3: -22883152599468032716
Sun Apr 10 19:52:41 2011 A4: -1029857547933
Sun Apr 10 19:52:41 2011 A5: 21420
Sun Apr 10 19:52:41 2011 skew 19100933.95, size 1.762e-14, alpha -9.607, combined = 5.916e-12 rroots = 5
[/code]

Never have I seen so large an alpha for a quintic.

Lucky strike from aliquot sequence 933436 - p48 with B1=1e6.
[CODE]
[Apr 17 2011, 14:46:16] Cofactor 273972725104359032346148865644845485140885599463271227581621122208261910596472612991851584100637 (96 digits)

<skip>
[Apr 17 2011, 15:06:19] c96: running 316 ecm curves at B1=1e6...
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2083437535
Step 1 took 6531ms
Step 2 took 2937ms
********** Factor found in step 2: 132783050676343724219193859450811356704120237019
[Apr 17 2011, 15:08:54] *** Neat 48-digit factor found: 132783050676343724219193859450811356704120237019
[Apr 17 2011, 15:08:54] *** prp48 = 132783050676343724219193859450811356704120237019

[Apr 17 2011, 15:08:54] Cofactor 2063310970103877012945364073856680410857686686823 (49 digits)
[Apr 17 2011, 15:08:54] *** prp49 = 2063310970103877012945364073856680410857686686823[/CODE]

The nicest splits I have ever found by SNFS:
[CODE]C154 of 365017^29-1
P77: 37396757234260224150408005834109810899214300392648561865731513695435673444773
P77: 42570463325362077428089614822023484513251325092204923997759805476493967955453

C146 of 182953^29-1
P73: 4722855254747137283734210892337977379933009090715325501938450326812074199
P73: 7951566854781719734008657015864299645598988203953685162383331394335376001[/CODE]

p55 with P+1
 

This one will be entered into the GCW tables soon enough but I thought it was worth recording here too.

GMP-ECM, running P+1 with B1=1G has just found the 55-digit factor 1273305908528677655311178780176836847652381142062038547 of GG(6,782).

It appears to be the second largest ever found by P+1

Paul

Here is p61 from aliquot sequence [URL="http://factordb.com/sequences.php?se=1&aq=11040"]11040[/URL] index 6357. I think it is second largest factor after fivemack's p65 from 3678 found by ECM in the aliquot project. Unfortunately it isn't large enough to enter top-10 of the year or top-50 all-the-time list.

[CODE]GMP-ECM 6.3 [configured with GMP 5.0.1 and --enable-asm-redc] [ECM]
Input number is 14468689114755261780062554686978294174162924920618844291513286842556497012589538616502354515650136548008914400095566281995954429761413127417 (140 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3152455236
Step 1 took 77947ms
Step 2 took 35108ms
********** Factor found in step 2: 2320325956091125553147342300714071593319445015822063254072069
Found probable prime factor of 61 digits: 2320325956091125553147342300714071593319445015822063254072069
[/CODE]

A P61 found by a curve at B1=11e6... nice :smile:

c155 from [URL="http://factordb.com/sequences.php?se=1&eff=2&aq=842592&action=last20&fr=0&to=100"]842592[/URL] index 7990 was cracked after hard ECM work on it: total curves count - 11000@43e6 and 10000@11e7.

[CODE]GMP-ECM 6.3 [configured with GMP 5.0.1 and --enable-asm-redc] [ECM]
Input number is 18476816107833387528013124067857437019638072238274560578069620015386142834793977613957035253413222160419640514669393339750389809776729202393893373019289189 (155 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1954032792
Step 1 took 737316ms
Step 2 took 191884ms
********** Factor found in step 2: 10049982157271241230892172732355293141849980921325639
Found probable prime factor of 53 digits: 10049982157271241230892172732355293141849980921325639[/CODE]