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
[/code]

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

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

[1] [url]https://www.mersenne.ca/exponent/110393069[/url]
[2] [url]https://www.mersenne.ca/manyfactors.php?s=n&o=d&exp_min=1&exp_max=999999967&fac_min=8&fac_max=20[/url]

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

[/CODE]Very lucky hit :smile:

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[/code] Splits into a P52 and P113:
[code]
16592224667024917579556227283455353404416196846072782288346763672507802677072819811820076100664585126995159009859
7437420132758649106672475593257347394141829965269339
[/code]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).

[QUOTE=UBR47K;537622]To my disappointment (yes, I should have continued ECM efforts), the C165 cofactor of step 41 of the A005265 sequence:[/QUOTE]

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.

167!-1 done
 

[code]
Fri Mar 20 19:48:18 2020 p78 factor: 339681113011636637534097684131750881577621867753623483183030698483021419238073
Fri Mar 20 19:48:18 2020 p104 factor: 20352452435868440772783919050239779605952424011217602415932301197691861381535113052414101488879148447221
[/code]

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
[/code]

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
[/code]

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
[/code]

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

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

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
[/CODE]

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.

[QUOTE=fivemack;540355]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.[/QUOTE]

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.

Got a bit lucky on [URL="http://www.factordb.com/index.php?id=1100000001504265849"]this[/URL] 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?