Near repdigit related numbers

News

I'm very pleased to report the factorization of the 279-digit number $N=(10^{279}-31)/3$.
$N$ splits as $N=\text{P126}\cdot\text{P153}$, where

$\text{P126}=683879988020855531843693974570809301443699094596561661475690616530795260027595121999433189270322605879651156172622984209245483$

and

$\text{P153}=487414954629682825615832070972614806528916687946252096353904135012248024359341728973161931019907828745530880376748837466333831896764672674769452527632481.$

Makoto Kamada estimates the time to factor this number at about "8314 CPU-days .. on 64-bit Opteron-2600MHz" and I confirm his estimation.

Results

composite digits date factor(s) method
$(10^{279}-31)/3$
a personal record
(size of factors and
snfs-difficulty)
279 Apr 28, 2018 $683879988020855531843693974570809301443699094596561661475690616530795260027595121999433189270322605879651156172622984209245483\cdot\text{P153}$ snfs
$(89\cdot10^{231}-53)/9$ 232 Apr 11, 2018 $131620463395982922779071123036879471286875895955571394068667$ snfs
$(83\cdot10^{205}+7)/9$ 144 Apr 10, 2018 $14484158243700009470879322204090426168500406613729967242716847909589$ gnfs
$(65\cdot10^{187}+7)/9$ 148 Mar 28, 2018 $16831840893591172568062336443752145698066070465644543066931807007$ snfs
$(47\cdot10^{187}-11)/9$ 149 Mar 27, 2018 $48328704791345992302621848217376195321160727166380358387$ snfs
$(58\cdot10^{231}-13)/9$ 231 Apr 23, 2017 $4023899318746439212971071540239479671887153874977868069805065525672688400316422571296627$ snfs
$(13\cdot10^{221}+41)/9$ 222 Mar 31, 2017 $3291659861208257158438545278634621322651960453818188143505937220725796048313$ snfs
$(7\cdot10^{224}-547)/9$ 224 Mar 29, 2017 $785926964213153898383872701807689146274048658637773089792275553$ snfs
$(47\cdot10^{220}+61)/9$ 221 Mar 28, 2017 $47070091947390813718645108799488852490845863085765872755847796788986863888655389$ snfs
$(25\cdot10^{220}+17)/3$ 221 Mar 11, 2017 $6954816965344570766584171447105027674009286277186597368481$ snfs
$(13\cdot10^{218}+41)/9$
a personal record
(size of factors)
219 Mar 4, 2017 $1986678560604733846358643845135592826608059500195201650031385071569608599534591180232772666674652352667$ snfs
$(47\cdot10^{217}+61)/9$ 218 Feb 25, 2017 $98196822291987017003179587967833368529376409955839$ snfs
$(637\cdot10^{215}-7)/9$ 217 Feb 21, 2017 $2899708525743448138750513834273051718459701701632174373080214267013049817300144137674371511$ snfs
$(49\cdot10^{213}+41)/9$ 214 Feb 8, 2017 $7664020863818392582730934287384539200365181891428879705383975143103380444381634498604233471151$ snfs
$(7\cdot10^{212}-277)/9$ 212 Feb 8, 2017 $2785454616304074829690351211386940330964587564748349550741274602199433$ snfs
$(4\cdot10^{231}+41)/9$ 231 Apr 2, 2017 $7344346423019282523689618364505761514549315503348692251043603$ snfs
$(7\cdot10^{223}-277)/9$ 223 Mar 28, 2017 $280644558775702659536145505776459915702225493602136282303542354089$ snfs
$(7\cdot10^{275}-27\cdot10^{137}-7)/9$
a personal record
(snfs-difficulty)
275 Oct 6, 2017 $17783338749850324659530314136241093884108150617292028363225235667$
$5728683950135865775006065633318050252133684586325264559163920687049979848681$
snfs
$(28\cdot10^{187}+71)/9$ 160 Nov 26, 2017 $239584981765857255141212284260634090180103103420501344594475562063454323$ snfs
$(10^{273}+72\cdot10^{136}-1)/9$ 273 Sep 26, 2016 $3948668030455486680577648190829312836176810875381268954494131$ ecm
$(10^{186}+29)/3$ 151 Oct 3, 2016 $13112828835004710777383762011092960660070699835638274668631$ snfs
$10^{186}-11$ 151 Oct 6, 2016 $22624205356454029235693793440315244373810753567981074765820580229437099$ snfs
$(10^{186}+449)/9$ 164 Oct 7, 2016 $101352994399302034756646044620801962432713950145931789343522847076508323387209261$ snfs
$(10^{243}+36\cdot10^{121}-1)/9$ 170 Oct 18, 2016 $118125788827754438742116816411737468123891789571$ ecm
$(10^{209}+18\cdot10^{104}-1)/9$ 174 Oct 19, 2016 $43979205777168314111876628821260607196683593$ ecm
$(10^{219}+18\cdot10^{109}-1)/9$ 176
132
Oct 29, 2016 $109208718222097569832577072616215064030627269$
$1495517513060797746420497391344488306663601104511650508044467647$
P-1
gnfs
$(10^{207}+18\cdot10^{103}-1)/9$ 188
142
Oct 29, 2016 $3724161603139849816143766890223038700947334723$
$3712578004916249190523260349678311450899510681449$
ecm
gnfs
$(10^{205}+18\cdot10^{102}-1)/9$ 190 Oct 31, 2016 $17655368062011612429586799534000607498665508790752438073560141899778613613$ snfs
$(10^{186}+119)/3$ 169 Oct 31, 2016 $638737564135088606309444305429242855028528236371260023294464111767065943331093$ snfs
$(10^{186}+629)/9$ 171 Nov 1, 2016 $19756594454463261794185050879211369844824666492884688407847121549$ snfs
$10^{203}-51$ 194 Dec 12, 2014 $16629961978036735475638234677858441872133187722741774227044570079292718835406643$ snfs
$10^{205}-51$ 165 Dec 14, 2014 $111858324016481002646110703768491429797295871915907398603336172365234693558249801$ snfs
$(10^{220}-51)/59$ 219 Dec 29, 2014 $1439459272170834402570373076314917151615716494246827879$
$2143714644424242485462961900706999641792727380193269378588362987458421539429$
snfs

Related links

factorization of near-repdigit-related numbers (Makoto Kamada)

database (Markus Tervooren)

Last update: April 28, 2018