Gratuitous factors thread - Page 45

chris2be8 · 2019-12-29, 16:34

Testing my scripts for GPU assisted factoring on (910^9*90^91-1)/77028940547131 I found:

Code:

p44 factor: 48393225443687462344070439622307205894087863
p46 factor: 4916170436419953361290051248613465047809496911
p48 factor: 640992308322487281162435458382965079411903857963
p54 factor: 249759862782190348678264306369685582086585744858182431

It had ECM to T40 run against it so it wasn't quite an ECM miss. But I've not had many 4 way splits.

Chris

SethTro · 2020-01-03, 18:16

I'm having great luck in 2020, I found another number with 10 known factors.

M110393069 has a factor: 2573045946551894438828660959 (P-1, B1=10000000, B2=1000000000, E=12)

This is only the 8th number with 10 known factors (and the 3rd below 1B)[2]

[1] https://www.mersenne.ca/exponent/110393069
[2] https://www.mersenne.ca/manyfactors....n=8&fac_max=20

unconnected · 2020-01-09, 10:53

Surprisingly big factor from aliquot sequence 159978:i10349:

Code:

GMP-ECM 7.0.4 [configured with GMP 6.1.2, --enable-asm-redc] [ECM]
Input number is 127417986331234894800947501788489152041099094751158669476175229712424483173302378926945822189256206042030876367999280926114962808939132577 (138 digits)
...
Run 26 out of 500:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1:941314382
Step 1 took 35101ms
Step 2 took 16395ms
********** Factor found in step 2: 94978631988367813736134774785157130018005660949036327
Found prime factor of 53 digits: 94978631988367813736134774785157130018005660949036327
Prime cofactor 1341543710029851568267813480042065650102760690386083130581576043504754316067577813751 has 85 digits

Very lucky hit

UBR47K · 2020-02-15, 04:01

To my disappointment (yes, I should have continued ECM efforts), the C165 cofactor of step 41 of the A005265 sequence:

Code:

123403345785785794973179663951809306414668826120744234869352839042890365928639504198664392743569755948605575707531021890910002244811989155367976608503485757491413201

Splits into a P52 and P113:

Code:

16592224667024917579556227283455353404416196846072782288346763672507802677072819811820076100664585126995159009859
7437420132758649106672475593257347394141829965269339

This was done with cado-nfs git-2cc8d725a3c8117e4e3a2329c1db6aa7b91cff1d and mariadb backend instead of sqlite (which resulted in crashes after every stage of the program) and some computers around (jobs had to be manually started since they would occasionally be used for other purposes).

R.D. Silverman · 2020-02-17, 01:41

Quote:

Originally Posted by UBR47K

To my disappointment (yes, I should have continued ECM efforts), the C165 cofactor of step 41 of the A005265 sequence:

No, you should not have continued ECM efforts. This would require testing to N^(1/3)
which is too much for ECM. N^(2/9) or perhaps n^(1/4) is recommended.

C165 is just too easy with NFS.

fivemack · 2020-03-21, 00:04

Code:

Fri Mar 20 19:48:18 2020  p78 factor: 339681113011636637534097684131750881577621867753623483183030698483021419238073
Fri Mar 20 19:48:18 2020  p104 factor: 20352452435868440772783919050239779605952424011217602415932301197691861381535113052414101488879148447221

5 Feb - 20 Mar for polsel, sieving and linear algebra using my local resources. CADO polynomial selection on six cores (12 threads) i7-4930K for 108 hours (c5=0..1M)

Code:

/home/nfsworld/cado-nfs-2.3.0/build/birch4/polyselect/polyselect -d 5 -P 4194304 -t 12 -admax 1000000 -admin 0 -incr 30 -nq 3125 -keep 100 -n 6913343695932187195199986268915183494976991949873051782625894833235576274732858487878860527814273973419645640871494975114191761102468143310283400616811115179277176508259534874245133 -v -v -v

91585177 thread-seconds sieving

Code:

Wed Mar 18 02:34:19 2020  found 70739021 hash collisions in 356237458 relations
Wed Mar 18 02:34:55 2020  commencing duplicate removal, pass 2
Wed Mar 18 02:37:52 2020  found 64922727 duplicates and 291314731 unique relations

57.9 hours for 19.83M matrix density-124 on 20 cores Xeon 4114

Code:

# Mon Mar  9 14:18:15 2020  skew 38830662.42, size 1.245e-17, alpha -6.229, combined = 8.183e-14 rroots = 5
n: 6913343695932187195199986268915183494976991949873051782625894833235576274732858487878860527814273973419645640871494975114191761102468143310283400616811115179277176508259534874245133
Y0: -136687615346877430400675876581222686
Y1: 45840668617947095861749
c0: -14417566742101902767835612012374200964842409
c1: 622800156875463432225590915386005985
c2: 73927713684054734964133822281
c3: -19818788008375212965
c4: -25936742859680
c5: 144900
skew: 38830662.417
lpbr: 32
lpba: 32
mfbr: 64
mfba: 96
rlambda: 2.6
alambda: 3.4
alim: 134000000
rlim: 134000000

Sieved 47M..138M (peak yield around 100M)

Batalov · 2020-03-21, 02:18

Congrats! What is next, (145!-1) cofactor ( = c185) ?

sean · 2020-03-21, 04:08

Thanks and congratulations! One less of these for me be hitting with ECM. It's quite big step to the next smallest:

For 145!-1 I have done 12335 curves with B1=850M.

Code:

Smallest composites:
  -: 145!-1 C185, 176!-1 C205, 136!-1 C214, 179!-1 C220, 139!-1 C222
  +: 169!+1 C193, 165!+1 C202, 172!+1 C205, 150!+1 C213, 176!+1 C215
First holes:
  -: 136!-1 C214, 139!-1 C222, 141!-1 C235, 145!-1 C185, 151!-1 C265
  +: 140!+1 C242, 146!+1 C223, 148!+1 C239, 150!+1 C213, 152!+1 C245

fivemack · 2020-03-21, 07:04

Currently running L4235A C201, which is going to take quite a while; will do 145!-1 after that. With the plague now and a baby due in June I doubt my hardware resources will grow in the next 18 months.

pinhodecarlos · 2020-03-21, 08:52

Quote:

Originally Posted by fivemack

Currently running L4235A C201, which is going to take quite a while; will do 145!-1 after that. With the plague now and a baby due in June I doubt my hardware resources will grow in the next 18 months.

Congrats on the baby, of course now family comes first, not this. Challenging weeks ahead please let us know if you need any kind of support.

MisterBitcoin · 2020-05-12, 18:15

Got a bit lucky on this P36 x P409 split, which is an factor from the generalised hyper woodall (90^374*374^90-1)/91.
Last remaining C440 is running, but i have no big hopes for an other factor so soon.

However, is there any list / project that works with them?

2019-12-29, 16:34	#485
chris2be8 Sep 2009 2·3·331 Posts	Testing my scripts for GPU assisted factoring on (910^9*90^91-1)/77028940547131 I found: Code: p44 factor: 48393225443687462344070439622307205894087863 p46 factor: 4916170436419953361290051248613465047809496911 p48 factor: 640992308322487281162435458382965079411903857963 p54 factor: 249759862782190348678264306369685582086585744858182431 It had ECM to T40 run against it so it wasn't quite an ECM miss. But I've not had many 4 way splits. Chris

2020-02-15, 04:01	#488
UBR47K Aug 2015 2·3·11 Posts	step=41 C165 cofactor, A005265 (Product of smallest prime factor minus 1, Startvalue = 3) GNFS To my disappointment (yes, I should have continued ECM efforts), the C165 cofactor of step 41 of the A005265 sequence: Code: 123403345785785794973179663951809306414668826120744234869352839042890365928639504198664392743569755948605575707531021890910002244811989155367976608503485757491413201 Splits into a P52 and P113: Code: 16592224667024917579556227283455353404416196846072782288346763672507802677072819811820076100664585126995159009859 7437420132758649106672475593257347394141829965269339 This was done with cado-nfs git-2cc8d725a3c8117e4e3a2329c1db6aa7b91cff1d and mariadb backend instead of sqlite (which resulted in crashes after every stage of the program) and some computers around (jobs had to be manually started since they would occasionally be used for other purposes). Last fiddled with by UBR47K on 2020-02-15 at 04:02

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2020-01-03, 18:16	#486
SethTro "Seth" Apr 2019 2²×59 Posts	I'm having great luck in 2020, I found another number with 10 known factors. M110393069 has a factor: 2573045946551894438828660959 (P-1, B1=10000000, B2=1000000000, E=12) This is only the 8th number with 10 known factors (and the 3rd below 1B)[2] [1] https://www.mersenne.ca/exponent/110393069 [2] https://www.mersenne.ca/manyfactors....n=8&fac_max=20

2020-03-21, 02:18	#491
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2⁴·3·193 Posts	Congrats! What is next, (145!-1) cofactor ( = c185) ?

2020-03-21, 07:04	#493
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 14353₈ Posts	Currently running L4235A C201, which is going to take quite a while; will do 145!-1 after that. With the plague now and a baby due in June I doubt my hardware resources will grow in the next 18 months.

2020-05-12, 18:15	#495
MisterBitcoin "Nuri, the dragon :P" Jul 2016 Good old Germany 787 Posts	Got a bit lucky on this P36 x P409 split, which is an factor from the generalised hyper woodall (90^374*374^90-1)/91. Last remaining C440 is running, but i have no big hopes for an other factor so soon. However, is there any list / project that works with them?