20191229, 16:34  #485 
Sep 2009
11110010101_{2} Posts 
Testing my scripts for GPU assisted factoring on (910^9*90^911)/77028940547131 I found:
Code:
p44 factor: 48393225443687462344070439622307205894087863 p46 factor: 4916170436419953361290051248613465047809496911 p48 factor: 640992308322487281162435458382965079411903857963 p54 factor: 249759862782190348678264306369685582086585744858182431 Chris 
20200103, 18:16  #486 
"Seth"
Apr 2019
2^{3}×5^{2} Posts 
I'm having great luck in 2020, I found another number with 10 known factors.
M110393069 has a factor: 2573045946551894438828660959 (P1, 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 
20200109, 10:53  #487 
May 2009
Russia, Moscow
2^{3}×313 Posts 
Surprisingly big factor from aliquot sequence 159978:i10349:
Code:
GMPECM 7.0.4 [configured with GMP 6.1.2, enableasmredc] [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 
20200215, 04:01  #488 
Aug 2015
40_{16} 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 Code:
16592224667024917579556227283455353404416196846072782288346763672507802677072819811820076100664585126995159009859 7437420132758649106672475593257347394141829965269339 Last fiddled with by UBR47K on 20200215 at 04:02 
20200217, 01:41  #489  
Nov 2003
2^{6}×113 Posts 
Quote:
which is too much for ECM. N^(2/9) or perhaps n^(1/4) is recommended. C165 is just too easy with NFS. 

20200321, 00:04  #490 
(loop (#_fork))
Feb 2006
Cambridge, England
6,323 Posts 
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:
/home/nfsworld/cadonfs2.3.0/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:
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:
# Mon Mar 9 14:18:15 2020 skew 38830662.42, size 1.245e17, alpha 6.229, combined = 8.183e14 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 Last fiddled with by fivemack on 20200323 at 11:57 
20200321, 02:18  #491 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×3×7×109 Posts 
Congrats! What is next, (145!1) cofactor ( = c185) ?

20200321, 04:08  #492 
Aug 2004
New Zealand
2^{2}·5·11 Posts 
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 Last fiddled with by sean on 20200321 at 04:10 
20200321, 07:04  #493 
(loop (#_fork))
Feb 2006
Cambridge, England
6,323 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.

20200321, 08:52  #494 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
3×37×43 Posts 
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.

20200512, 18:15  #495 
"Nuri, the dragon :P"
Jul 2016
Good old Germany
2·7·53 Posts 
Got a bit lucky on this P36 x P409 split, which is an factor from the generalised hyper woodall (90^374*374^901)/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? 
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