- Last update: Sep 04, 2026
- Found by YOYO@home/marginal_2001
Sep 03, 2026 n =3180M: 20953821829826023101286848610267141432836817568064575641; ecm: B1 =2.9e9; sigma: 0:14772142859422438365
- Found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner
Sep 03, 2026 n = 477: 264325393858573053034128648181202531414568796061070622864135564291201; SNFS
R477/c252: SNFS-difficulty = 318;
Msieve v. 1.54 (SVN Unversioned directory)
random seeds: 7861c62b 2e8c0e17
Using 36 OpenMP threads
factoring 321423416108511758956024449794771161415777114306940078273538586684357414093357428237590680378849999269383156706373943304468499931366024821786732799014502107091272518773703758431005092360962844504496614070388161984515737691570040764150018243235817821879 (252 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (252-digit input)
R0: -100000000000000000000000000000000000000000000000000000
R1: 1
A0: 1
A1: 0
A2: 0
A3: 1
A4: 0
A5: 0
A6: 1
skew 1.38, size 1.634e-15, alpha 1.996, combined = 7.744e-16 rroots = 0
commencing relation filtering
estimated available RAM is 193222.6 MB
commencing duplicate removal, pass 1
error -15 reading relation 2229418581
...
skipped 1082088 relations with b > 2^32
skipped 26 relations with composite factors
skipped 14 malformed relations
found 135725341 hash collisions in 2894081343 relations
added 1417 free relations
commencing duplicate removal, pass 2
found 24210590 duplicates and 2869872169 unique relations
memory use: 8870.0 MB
reading ideals above 1332543488
commencing singleton removal, initial pass
memory use: 41024.0 MB
reading all ideals from disk
memory use: 75443.6 MB
commencing in-memory singleton removal
begin with 2869872169 relations and 2350882452 unique ideals
reduce to 1956744498 relations and 1351239388 ideals in 14 passes
max relations containing the same ideal: 39
reading ideals above 720000
...
commencing in-memory singleton removal
begin with 278434271 relations and 271662438 unique ideals
reduce to 278254482 relations and 265400397 ideals in 7 passes
max relations containing the same ideal: 65
removing 1709789 relations and 1388806 ideals in 320983 cliques
commencing in-memory singleton removal
begin with 276544693 relations and 265400397 unique ideals
reduce to 276537971 relations and 264004864 ideals in 5 passes
max relations containing the same ideal: 65
relations with 0 large ideals: 805537
relations with 1 large ideals: 839459
relations with 2 large ideals: 6237471
relations with 3 large ideals: 24210772
relations with 4 large ideals: 53829776
relations with 5 large ideals: 73407589
relations with 6 large ideals: 63735884
relations with 7+ large ideals: 53471483
commencing 2-way merge
reduce to 173245881 relation sets and 160712774 unique ideals
commencing full merge
memory use: 19114.6 MB
found 89217639 cycles, need 87490974
weight of 87490974 cycles is about 7874464616 (90.00/cycle)
distribution of cycle lengths:
1 relations: 8427674
2 relations: 8264611
3 relations: 8795643
4 relations: 8782224
5 relations: 8713071
6 relations: 8342083
7 relations: 7701601
8 relations: 6846569
9 relations: 5835558
10+ relations: 15781940
heaviest cycle: 20 relations
commencing cycle optimization
start with 525954854 relations
pruned 14534476 relations
memory use: 16729.1 MB
distribution of cycle lengths:
1 relations: 8427674
2 relations: 8443514
3 relations: 9117089
4 relations: 9059943
5 relations: 9030867
6 relations: 8596780
7 relations: 7931327
8 relations: 6964616
9 relations: 5860214
10+ relations: 14058950
heaviest cycle: 20 relations
RelProcTime: 565871
elapsed time 157:12:58
commencing linear algebra
using VBITS=256
matrix starts at (0, 0)
matrix is 87470028 x 87470195 (32570.8 MB) with weight 9321533112 (106.57/col)
sparse part has weight 7576055130 (86.61/col)
saving the first 240 matrix rows for later
matrix includes 256 packed rows
matrix is 87469788 x 87470195 (30788.9 MB) with weight 6972368445 (79.71/col)
sparse part has weight 6671602090 (76.27/col)
using block size 8192 and superblock size 608256 for processor cache size 25344 kB
commencing Lanczos iteration (36 threads)
memory use: 47224.0 MB
restarting at iteration 220973 (dim = 56400069)
linear algebra at 64.5%, ETA 662h14m
checking every 10000 dimensions, checkpointing every 80000 dimensions
lanczos halted after 342707 iterations (dim = 87469784)
recovered 36 nontrivial dependencies
BLanczosTime: 2224170
commencing square root phase
reading relations for dependency 1
read 43735632 cycles
cycles contain 135310588 unique relations
read 135310588 relations
multiplying 135310588 relations
multiply complete, coefficients have about 3839.55 million bits
initial square root is modulo 408843947
sqrtTime: 10741
p69 factor: 264325393858573053034128648181202531414568796061070622864135564291201
p184 factor: 1216014138545042426146100451447034631004763897044361520224119802411417027642329288384430088111832831908816824946425421818071911957002330047322512752032016992082391900763747247208417079
elapsed time 02:59:02
- Found by Alfred Eichhorn
Aug 27, 2026 n =71777: 156456403920536358986115721; ecm: B1 = 1e6; sigma: 7837148007233723
Aug 27, 2026 n =72089: 492155699801093269795612858721; ecm: B1 = 1e6; sigma: 9011785328192578
- Found by Kurt Beschorner
Aug 27, 2026 n =11039: 4633606765585495795628349639479; ecm: B1 = 1e6; sigma: 2055547419375831
Aug 27, 2026 n =11040: 86896780112925482149032963622396560961; ecm: B1 = 5e6; sigma: 2840821663125905
Aug 27, 2026 n =11043: 1531097846027243253608757419128573; ecm: B1 = 1e6; sigma: 5417008376434069
Aug 27, 2026 n =11043: 145001339222897334260000321176371769; ecm: B1 = 1e6; sigma: 2563673747780688
Aug 27, 2026 n =11050: 12369051090149642172465475195000651325801; ecm: B1 = 3e6; sigma: 6768654463712671
Aug 27, 2026 n =11053: 304139100693650797603705267627; ecm: B1 = 1e6; sigma: 8216917133303096
Aug 27, 2026 n =11055: 6243216491699144214161041997311; ecm: B1 = 1e6; sigma: 2049953487299892
Aug 27, 2026 n =11061: 21038064804877783178463943427911; ecm: B1 = 1e6; sigma: 2388049792477092
Aug 27, 2026 n =11063: 4185919043642456658879477497791; ecm: B1 = 1e6; sigma: 3132618928180128
Aug 27, 2026 n =11077: 1279627919999270412710836203761; ecm: B1 = 1e6; sigma: 3969653936579497
- Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner
Aug 24, 2026 R567/c287: SNFS-difficulty = 324;
565M unique raw relations are collected;
currently progress 19.7%;
- Found by Kurt Beschorner
Aug 16, 2026 n =4100M: 613147347674628012609076766868745938781747501; ecm: B1 =43e6; sigma: 2825754950895789
Aug 16, 2026 n =11022: 15285659517712849659334646442109099; ecm: B1 = 5e6; sigma: 8451230280482068
Aug 16, 2026 n =11028: 6575760682755470241764235361478749; ecm: B1 = 3e6; sigma: 114918809848742
Aug 16, 2026 n =12330: 1598868175698987229754422816040533441; ecm: B1 = 5e6; sigma: 3949108578646975
Aug 16, 2026 n =12337: 3042670847015129133696713613521; ecm: B1 = 1e6; sigma: 6028446040571788
- Found by Alfred Eichhorn
Aug 15, 2026 n =63149: 731197287945862250521096871; ecm: B1 = 1e6; sigma: 0:8618785652602297
Aug 15, 2026 n =71549: 18379709699773367960014327997; ecm: B1 = 1e6; sigma: 0:1007016806845147
Aug 15, 2026 n =71569: 9132447865959263943735632521883; ecm: B1 = 1e6; sigma: 0:6661750315960354
- Found by Kurt Beschorner
Aug 05, 2026 n = 3014: 3224257283821690911882860343913279673197968001; ecm: B1 =20e6; sigma: 346575584497108
Aug 05, 2026 n =11015: 38361476883252040573781321; ecm: B1 = 1e6; sigma: 5117826424394022
Aug 05, 2026 n =12295: 484743392732493780746667717991; ecm: B1 = 1e6; sigma: 1522186952526259
Aug 05, 2026 n =12307: 333374801444055325819386005205439; ecm: B1 = 1e6; sigma: 5919142273543134
Aug 05, 2026 n =12328: 1485186211524993980332189457327993; ecm: B1 =1.5e6; sigma: 8456453911070310
- Found by Alfred Eichhorn
Jul 26, 2026 n =33083: 6675715261589480685252905491003; ecm: B1 = 1e6; sigma: 0:8131647610823038
Jul 26, 2026 n =70997: 12569762063305598037002812395517; ecm: B1 = 1e6; sigma: 0:7572621526288766
Jul 26, 2026 n =71011: 994162421596480115595396227; ecm: B1 = 1e6; sigma: 0:4672737597017891
- Found by Alfred Eichhorn
Jul 09, 2026 n =59809: 2974461269600365487438093421721; ecm: B1 = 1e6; sigma: 0:6930322239139690
Jul 09, 2026 n =62633: 4770048381930236202807868411187; ecm: B1 = 1e6; sigma: 0:4102478440982954
Jul 09, 2026 n =62987: 285189180407754140621972589923; ecm: B1 = 1e6; sigma: =0:4048756822361665
Jul 09, 2026 n =70039: 4515288873284468441685842687867; ecm: B1 = 1e6; sigma: 0:6070592813061543
Jul 09, 2026 n =70241: 510387445962916661797514671; ecm: B1 = 1e6; sigma: 0:582790225641299
- Found by YOYO@home/Schildkroete
Jun 26, 2026 n =3420M: 11910496620270230227967351103984592528826219533871461; ecm: B1 = 850e6; sigma: 0:14888554157636030172
- Found by Alfred Eichhorn
Jun 22, 2026 n =59441: 658830707682755169056044723; ecm: B1 = 1e6; sigma: 0:6996752501839657
Jun 22, 2026 n =59471: 190815741323077589216921714573; ecm: B1 = 1e6; sigma: 0:7404090761943369
Jun 22, 2026 n =59539: 135548153477087092759519855361; ecm: B1 = 1e6; sigma: 0:5707363897398941
- Found by Kurt Beschorner
Jun 22, 2026 n = 3016: 79745540397089767290902971445484579513353729; ecm: B1 =20e6; sigma: 2848204528186435
Jun 22, 2026 n =12278: 1045177907460420329867780401133867851; ecm: B1 =1.5e6; sigma: 4051930692612612
Jun 22, 2026 n =12279: 9637219349226698572164080730659317; ecm: B1 = 1e6; sigma: 7164493398039665
Jun 22, 2026 n =12324: 32860792314779471409511216930296349; ecm: B1 = 3e6; sigma: 309243589456182
- Found by Kurt Beschorner
Jun 17, 2026 n = 3017: 49473518867236296999163440070344126523; ecm: B1 =11e6; sigma: 5943577211292700
Jun 17, 2026 n =12320: 12387457044434846313038653536577732392641; ecm: B1 = 3e6; sigma: 383306035719674
Jun 17, 2026 n =12321: 98481601921708468998211578895369; ecm: B1 = 1e6; sigma: 1985997901299033
- Found by Alfred Eichhorn
May 29, 2026 n =32507: 2300930380372305197566072049639; ecm: B1 = 1e6; sigma: 0:7501853553690321
- Found by Kurt Beschorner
May 29, 2026 n = 1946: 27554793188997041736632096781280014586232237622274391333; ecm: B1 =30e6; sigma: 2268919098670077
May 29, 2026 n =33624: 421521330863204485354297; P-1: B1 =120e6
May 29, 2026 n =33624: 12796650901118026271423089; P-1: B1 =120e6
May 29, 2026 n=100870: 595613554200944189681; P-1: B1 =120e6
- Found by Kurt Beschorner
May 19, 2026 n = 1946: 1141091827346082725563186077734683523890652491324921; ecm: B1 =30e6; sigma: 2391699717520293
May 19, 2026 n = 1948: 1245574263344236926178624905967619777496826201; ecm: B1 =30e6; sigma: 298681832424430
May 19, 2026 n =15109: 3126121653732181949392727677; P-1: B1 =330e6
May 19, 2026 n=100851: 1331119777281831087651429151; P-1: B1 = 50e6
May 19, 2026 n=100852: 35480851910324239338266251369; P-1: B1 =120e6
May 19, 2026 n=100855: 3630007311475118671; P-1: B1 = 55e6
May 19, 2026 n=100863: 1015929284756244359406737203; P-1: B1 = 55e6
May 19, 2026 n=100863: 2537548873731441460658709523; P-1: B1 = 55e6
- Found by Alfred Eichhorn
May 17, 2026 n =58043: 2462878157842741990086979241; ecm: B1 = 1e6; sigma: 5913375008734535
May 17, 2026 n =58231: 8591284841513196276725154917039; ecm: B1 = 1e6; sigma: 0:4677710267393855
- Found by Kurt Beschorner
May 11, 2026 n = 1939: 2319804043020569784657764982312066706540009; ecm: B1 =20e6; sigma: 1141204615990357
May 11, 2026 n = 2370: 482449202423416486767475769973056969504388721; ecm: B1 =43e6; sigma: 1028291333
May 11, 2026 n =12271: 228199770997052675993096122519371289; ecm: B1 = 1e6; sigma: 4270726391921522
May 11, 2026 n =12275: 4409632003308300498889025067767487751; ecm: B1 = 1e6; sigma: 7126292361183199
May 11, 2026 n =12277: 118409763548324573394163349399; ecm: B1 = 1e6; sigma: 865464314463046
May 11, 2026 n =20168: 36413245003538692345629330721; P-1: B1 =120e6
May 11, 2026 n=100833: 218914320925344172603; P-1: B1 = 50e6
May 11, 2026 n=100840: 26923763855635207088748001; P-1: B1 =120e6
May 11, 2026 n=100841: 263521074163247213; P-1: B1 = 50e6
May 11, 2026 n=100841: 1747747951842195723733; P-1: B1 = 50e6
May 11, 2026 n=100849: 837394980053163708359; P-1: B1 = 50e6
- Found by Kurt Beschorner
Apr 28, 2026 n = 4079: 426915461085826624259143920722034774479; ecm: B1 = 1e6; sigma: 7104292139681039
Apr 28, 2026 n =12223: 6369097247405237468604340064437; ecm: B1 = 1e6; sigma: 4266251454290015
Apr 28, 2026 n =12233: 22472722653715903146492540430914710329; ecm: B1 = 1e6; sigma: 4346254638954307
Apr 28, 2026 n =12247: 2776545656296308111024907187; ecm: B1 = 1e6; sigma: 5666394773832634
Apr 28, 2026 n =12250: 621878902495839421287137521938451694251; ecm: B1 = 3e6; sigma: 5389300061366745
Apr 28, 2026 n =12264: 3141173557231484342233218217422101569; ecm: B1 = 5e6; sigma: 3950502677650097
- Found by Alfred Eichhorn
Apr 27, 2026 n =57077: 3848471893272271808963508973; ecm: B1 = 1e6; sigma: 0:4742462032411031
Apr 27, 2026 n =61469: 698138979099137779882713720563; ecm: B1 = 1e6; sigma: 7844869317150916
Apr 27, 2026 n =61519: 3592374185368400157663594959; ecm: B1 = 1e6; sigma: 0:2912591680432495
- Found by Kurt Beschorner
Apr 27, 2026 n = 1909: 225703566525345000237290241654276163965649; ecm: B1 =20e6; sigma: 5168216469123288
Apr 27, 2026 n =12240: 263000468346705414367562319148772641; ecm: B1 = 3e6; sigma: 4513911137171856
Apr 27, 2026 n =12256: 43376467754503927150112444601064993; ecm: B1 =1.5e6; sigma: 6872108156273792
Apr 27, 2026 n =20163: 721292645808181608827351401; P-1: B1 = 50e6
Apr 27, 2026 n =33606: 230893953674075061463927; P-1: B1 =120e6
Apr 27, 2026 n =33607: 5964387365159475570403; P-1: B1 = 50e6
Apr 27, 2026 n =33609: 48248595085802769587549417191; P-1: B1 = 50e6
Apr 27, 2026 n=100814: 776396116921274123891; P-1: B1 =120e6
Apr 27, 2026 n=100818: 54821518733674447939; P-1: B1 =120e6
Apr 27, 2026 n=100822: 8152588103725941068097397481; P-1: B1 =120e6
Apr 27, 2026 n=100830: 394392699271528282561; P-1: B1 =120e6
- Found by NFS@home
Apr 26, 2026 n = 784: 289541217302474902147738712574747645681665598761448687795987839125906245176246519610151449976343537460699905766689; SNFS
- Found by Kurt Beschorner
Apr 09, 2026 n =12183: 109821907852656265834529348424560071; ecm: B1 = 1e6; sigma: 7051987285101674
Apr 09, 2026 n =12185: 130322056866604174556330887201; ecm: B1 = 1e6; sigma: 2275484587771368
Apr 09, 2026 n =12187: 4331894187607779562471947940622489759; ecm: B1 = 1e6; sigma: 899074588164263
Apr 09, 2026 n =12197: 281192396724953094378341698240982668717; ecm: B1 = 1e6; sigma: 1544402678692367
Apr 09, 2026 n =12198: 100121059314668298378348902933673188089; ecm: B1 = 3e6; sigma: 6858696947538165
Apr 09, 2026 n =12199: 1739280392832343482352334226643081; ecm: B1 = 1e6; sigma: 1208315919345894
Apr 09, 2026 n =12201: 109836927317630094632408443; ecm: B1 = 1e6; sigma: 3736292984657857
Apr 09, 2026 n=12220L: 6973238477503511321447740394630472080633701; ecm: B1 =11e6; sigma: 1197379811455370
Apr 09, 2026 n= 33604: 291531278012433218181442837529809; P-1: B1 =120e6
Apr 09, 2026 n=100807: 760773901018618018808663640224203; P-1: B1 = 50e6
- Found by Alfred Eichhorn
Mar 30, 2026 n =61099: 155172907171674539481224758667; ecm: B1 = 1e6; sigma: 7431135821234599
| ECM efforts | |
|---|---|
| with Rn: 1 < n < 2000 (Sep 04, 2026) | with Rn: 1999 < n < 3000 (Aug 16, 2026) |
| with Rn: 2999 < n < 4000 (Sep 04, 2026) | with Rn: 3999 < n < 5000 (Aug 24, 2026) |
| with Rn: 4999 < n < 6000 (Aug 15, 2026) | with Rn: 5999 < n < 7000 (Feb 12, 2026) |
| with Rn: 6999 < n < 8000 (Jul 20, 2026) | with Rn: 7999 < n < 9000 (Aug 05, 2026) |
| with Rn: 8999 < n <10000 (Jul 26, 2026) | with Rn: 9999 < n <11000 (Aug 05, 2026) |
| with Rn: 10999 < n <12000 (Sep 04, 2026) | with Rn: 11999 < n <14980L/M (Sep 04, 2026) |
| currently ECM-efforts by yoyo@home: ecm-curves | |||||
|---|---|---|---|---|---|
| B1 = 11e7/17000 curves/ numbers < 951 digits |
737 in progress |
.... in progress |
.... in progress |
.... in progress |
.... in progress |
| B1 = 26e7/42000 curves/ numbers < 650 digits |
607 in progress |
611 in progress |
713 in progress |
775 in progress |
1280 in progress |
| B1 = 85e7/70000 curves/ numbers < 400 digits |
1332 in progress |
1656 in progress |
.... in progress |
.... in progress |
.... in progress |
| B1 = 29e8/nnnn curves/ numbers < 400 digits |
1164 in progress |
1236 in progress |
1722 in progress |
.... in progress |
.... in progress |
| Factorizations | |
|---|---|
| Repunits: R1 - R2500 (Sep 03, 2026) | Repunits: R2501 - R5000 (Sep 04, 2026) |
| Repunits: R5001 - R7500 (Feb 11, 2026) | Repunits: R7501 - R10000 (Aug 05, 2026) |
| Repunits: R10001 - R12500 (Aug 27, 2026) | Repunits: R12501 - R14980L/M (Apr 09, 2026) |
| Exponent | Primes/PRP found by ... |
| - 10ˆ10 | R2 = prime |
| - 10ˆ20 | R19 = prime |
| - 10ˆ100 | R23 = prime |
| - 10ˆ1000 | R317 = prime |
| - 10ˆ10000 | R1031 = prime WD (Dec 1985) |
| - 10ˆ50000 | R49081 = prime Paul Underwood (Mar 2022) |
| - 10ˆ100000 | R86453 = prime Andreas Enge (May 15, 2023) |
| - 10ˆ250000 | R109297 = prime A. Enge/P. Underwood (May 2025) |
| - 10ˆ500000 | R270343 = PRP Maksym Voznyy - Anton Budnyy (Jul 2007) |
| - 10ˆ7500000 | R5794777 = PRP S. Batalov - Ryan Propper (Apr 2021) |
| - 10ˆ10000000 | R8177207 = PRP S. Batalov - Ryan Propper (May 2021) |