I've noticed that Φ[SUB]3[/SUB](Φ[SUB]3[/SUB](n)) could be factored by SNFS with the polynomial x^4 + 2*x^3 + 4*x^2 + 3*x + 3, x = n. So I searched Pascal's tXXX.txt files but could find only one composite to play with. It's a C124 from t800.txt:

[CODE]Φ[SUB]3[/SUB](Φ[SUB]3[/SUB](494816894793945434195756741367539))
= σ(244843759373522464138800829966383113629900505470123750552624284061^2)
P60: 581313171033503903486387923011255412473644317217878483590121
P64: 4920021986526868171859523304779754644784332407147940901429749121[/CODE]
By GNFS, this number would be about 20 times harder.

I plan to factor more numbers of this form from Pascal's checkfacts.txt.

2 Factors I found the last weeks.

The first one is from 149^149-1, only one composite of 137 digits is left now at this number. I made ECM on this C137 up to 75% of T50, but maybe that number could be sieved out by someone (still to large for my ressources).
[CODE]GMP-ECM 6.1.3 [powered by GMP 4.2.2] [ECM]
Input number is (149^149-1)/148/1193/51784951/450090559/465814231/16400487241407243385146121137075484835648069406803562771129954315766789617076024288801802046796652400409959000416610079753541151023163581 (158 digits)
Run ~3100:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=550617036
Step 1 took 234484ms
Step 2 took 84938ms
********** Factor found in step 2: 14897084928588789671974072568141537826492971
Found probable prime factor of 44 digits: 14897084928588789671974072568141537826492971
Probable prime cofactor ((149^149-1)/148/1193/51784951/450090559/465814231/16400487241407243385146121137075484835648069406803562771129954315766789617076024288801802046796652400409959000416610079753541151023163581)/14897084928588789671974072568141537826492971 has 115 digits
[/CODE]The second factor I found with Alex' extension for prime95, I wantet to know if this extension is still useable if the number is not a Mersenne-number. Thus I run 4 stage 1 (B1=44e6) with prime95 and resumed them with GMP-ECM (B2=5e11).
[CODE]11/02/06, 193^193-1 finished
N=0x19328035714E85A269C60F7535859AD53FCA33360B18795207D3D6916E4DEAB28EA30FDC4A6980A4CA95A5EBFE8139D6349A35D83BEF3E1A0ECF0B765F6DCE1EFF24E3A1A066CF095C5F1058FECABE1F1C560EC9E8AD82ED; QX=0x58979B5D50E9E9619498E33F1FEE0F77E1B0A5EBDBC6F0292E046916F5373F00461C160BF7349B9E43E278193D2B8908751195679161F43254CD904CCFF1028C36064F13A061BC9A2137BAAFFDA2049440997C748717823; SIGMA=3943874793214385
GMP-ECM 6.3 [configured with GMP 5.0.1 and --enable-asm-redc] [ECM]
Resuming ECM residue saved with Prime95
Input number is 0x19328035714E85A269C60F7535859AD53FCA33360B18795207D3D6916E4DEAB28EA30FDC4A6980A4CA95A5EBFE8139D6349A35D83BEF3E1A0ECF0B765F6DCE1EFF24E3A1A066CF095C5F1058FECABE1F1C560EC9E8AD82ED (211 digits)
Using MODMULN
Using B1=1, B2=582118959250, polynomial Dickson(30), sigma=3943874793214385
dF=131072, k=3, d=1345890, d2=11, i0=-10
Expected number of curves to find a factor of n digits:
35 40 45 50 55 60 65 70 75 80
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Step 1 took 0ms
Using 49 small primes for NTT
Estimated memory usage: 548M
Initializing tables of differences for F took 1716ms
Computing roots of F took 62354ms
Building F from its roots took 26099ms
Computing 1/F took 10499ms
Initializing table of differences for G took 1404ms
Computing roots of G took 52245ms
Building G from its roots took 25958ms
Computing roots of G took 52526ms
Building G from its roots took 26270ms
Computing G * H took 5164ms
Reducing G * H mod F took 5475ms
Computing roots of G took 52760ms
Building G from its roots took 26161ms
Computing G * H took 5195ms
Reducing G * H mod F took 5476ms
Computing polyeval(F,G) took 50623ms
Computing product of all F(g_i) took 296ms
Step 2 took 410891ms
********** Factor found in step 2: 10782947738432352654873470446407092959346090456667431
Found probable prime factor of 53 digits: 10782947738432352654873470446407092959346090456667431
Probable prime cofactor (0x19328035714E85A269C60F7535859AD53FCA33360B18795207D3D6916E4DEAB28EA30FDC4A6980A4CA95A5EBFE8139D6349A35D83BEF3E1A0ECF0B765F6DCE1EFF24E3A1A066CF095C5F1058FECABE1F1C560EC9E8AD82ED)/10782947738432352654873470446407092959346090456667431 has 159 digits[/CODE]The factor finished 193^193-1.

As I said, I tried to factor the C137 of 149^149-1 for a long time, maybe there is someone out there who is able to gnfs it. I would spend some time for sieving, of course.

greetings
Matthias

Hi Matthias.

A C137 takes 250 CPU-hours to sieve on a machine of mine which would run one ECM curve on your number in 67 seconds (IE about 4.8 times as fast as yours); so you could run the GNFS in not much over one hundred days, whilst you've spent twelve days running curves.

[QUOTE=fivemack;251704]Hi Matthias.

A C137 takes 250 CPU-hours to sieve on a machine of mine which would run one ECM curve on your number in 67 seconds (IE about 4.8 times as fast as yours); so you could run the GNFS in not much over one hundred days, whilst you've spent twelve days running curves.[/QUOTE]
if I understand you correct, you suggest to run more ECM on the C137. OK, I will finish the T50 size and maybe start some curves B1=110e6 on it. I will post again if that is done.
Thanks for your estimation.

greetings
Matthias

I am sorry if I am being unclear; I'm suggesting only that you probably do have the resources to do GNFS on the C137.

Though, if you ask factordb, it tells you that 149^149-1 has already been factorised, so I would recommend that you do no more work on the C137. The factor you want is probably 24356237167368011037018270166971738740925336580189261

[QUOTE=fivemack;251713]I am sorry if I am being unclear; I'm suggesting only that you probably do have the resources to do GNFS on the C137.

Though, if you ask factordb, it tells you that 149^149-1 has already been factorised, so I would recommend that you do no more work on the C137. The factor you want is probably 24356237167368011037018270166971738740925336580189261[/QUOTE]

Ops, I haven't seen this factor before... I added the P44 as a factor appr. in June last year to the db, at that time the P53 wasn't known...OK, I marked the number as done in my list, thank you for the hint.

About the ressources. I only have 4 GB of memory on my i5-750 running with Win7-32 bit. How much memory is needed to run the block lanczos on a C137? (Or which size is possible to factor with 4GB of RAM)?

greetings
Matthias

I am currently running block Lanczos for a C166 and it's using less than 3.5GB of memory. A C137 uses I believe well under 1GB.

But you really ought to be running a 64-bit OS; I can run one gmp-ecm curve with the parameters you posted in 64 seconds on my iMac with an i5/750 processor, so you're losing a factor five of performance by running 32-bit Windows.

IIRC, I obtained the factors of 149^149-1 (among others) from a recent paper by Wagstaff, et al. and entered them to the database.

[QUOTE=Zeta-Flux;250877]Pascal or William,

Do either of you have the full factorization of: [code][(195163150047313020008802835877656364030813707064261)^5-1]/[195163150047313020008802835877656364030813707064261-1] ?[/code]

Thanks,
Zeta-Flux[/QUOTE]

I've done 1000 curves at B1=260M on this number. No factor found.

I've done 5000 curves at B1=260M on each of 13^269-1, 547^107-1, 2801^83-1. No factor found.

RSALS has started SNFS on the following number, requested by Zeta-Flux in this thread.
[code](195163150047313020008802835877656364030813707064261)^5-1]/[195163150047313020008802835877656364030813707064261-1][/code]