M8 627 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	400000000	400000000	0.0707	29.9840%	0.0707	29.9840%
Target	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.2076%	0.0003	68.5661%
Difference	-44	-0.0003	-68.1818%	+399999500	+399990000	+0.0707	+28.7764%	+0.0705	-38.5820%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8627	123348847	9	26.878	7149 3 × 2383	-	3	2383	1.604e-9	2.346e-8	4.285e-8
8627	1429764598007	13	40.379	82865689 523 × 158443	-	523	158443	2.201e-5	1.614e-6	2.851e-6
8627	6675871535988671	16	52.568	386917325605 5 × 29 × 127 × 21010987	-	127	21010987	0.1304	0.0002	0.0004
8627	199774133443790513	18	57.471	11578424333128 2³ × 1447303041641	-	8	1447303041641	2.3545	13.943	26.041
8627	419109812630427361	18	58.540	24290588421840 2⁴ × 3 × 5 × 13 × 23 × 3853 × 87853	-	3853	87853	7.1676	1.491e-6	1.581e-6
8627	617439464973514186509350238353	30	98.962	35785294133158350904680088 2³ × 7 × 17 × 1848589 × 20334208781772121	-	1848589	20334208781772121	1.425e+13	195,892	365,871

exponent	prime factors	composite factor	digits	bits*
8627	123348847 1429764598007	176359814645581947929	21	67.257
8627	123348847 6675871535988671	823461056684321572912337	24	79.446
8627	123348847 199774133443790513	24641909020715699088088511	26	84.349
8627	123348847 419109812630427361	51696712154349252096602767	26	85.418
8627	1429764598007 6675871535988671	9544924782999215825621178697	28	92.947
8627	1429764598007 199774133443790513	285629983595457917349765307591	30	97.850
8627	1429764598007 419109812630427361	599228372776332067056778869527	30	98.919
8627	6675871535988671 199774133443790513	1333666451084203500525753265278223	34	110.039
8627	6675871535988671 419109812630427361	2797923268593015211748206384427231	34	111.108
8627	199774133443790513 419109812630427361	83727299636033034213844250947426193	35	116.011
8627	123348847 1429764598007 6675871535988671	1177355466684678473994525451055912359	37	119.825
8627	123348847 1429764598007 199774133443790513	35232129145128648542114846411950197577	38	124.728
8627	123348847 1429764598007 419109812630427361	73914128871646749360580357090118885369	38	125.797
8627	123348847 617439464973514186509350238353	76160446096779860444071306620017728991	38	125.840
8627	123348847 6675871535988671 199774133443790513	164506219023818401703215559078553941258881	42	136.917
8627	123348847 6675871535988671 419109812630427361	345120609175419738622602111837137699252657	42	137.986
8627	1429764598007 617439464973514186509350238353	882793088431513667776652766085546678762471	42	139.341
8627	123348847 199774133443790513 419109812630427361	10327665872528194424189239791943678524149471	44	142.889
8627	1429764598007 6675871535988671 199774133443790513	1906829077309828547236985830481386138606301561	46	150.418
8627	1429764598007 6675871535988671 419109812630427361	4000371637374323882713210284933870835659128617	46	151.487
8627	6675871535988671 617439464973514186509350238353	4121946549412757379911281511856643791357698863	46	151.530
8627	1429764598007 199774133443790513 419109812630427361	119710328906324408574929502729954839725947397351	48	156.390
8627	199774133443790513 617439464973514186509350238353	123348434069081441480147132504076144524350145089	48	156.433
8627	419109812630427361 617439464973514186509350238353	258774938475680848167771198135432492225602776433	48	157.502
8627	123348847 1429764598007 617439464973514186509350238353	10889150959759624938499117221601288619003018472093 7	51	166.219
8627	6675871535988671 199774133443790513 419109812630427361	55895269642538754648634035379255491279055905665950 3	51	168.579
8627	123348847 1429764598007 6675871535988671 199774133443790513	23520516811224121306936723794521643515886948448365 0167	54	177.296
8627	123348847 1429764598007 6675871535988671 419109812630427361	49344122904162495833723772031513443882547999993165 4599	54	178.365
8627	123348847 6675871535988671 617439464973514186509350238353	50843735426569214990279753677993384095368071932426 0961	54	178.408
8627	123348847 1429764598007 199774133443790513 419109812630427361	14766131044585886805674467268023281842265407445896 704297	56	183.268
8627	123348847 199774133443790513 617439464973514186509350238353	15214887121676714155674122184734015227283953821010 862383	56	183.312
8627	123348847 419109812630427361 617439464973514186509350238353	31919590293471170161476639849814147762364566353009 322751	56	184.380
8627	1429764598007 6675871535988671 617439464973514186509350238353	58934132512274718172062759881239255145627326956017 55966041	58	191.909
8627	123348847 6675871535988671 199774133443790513 419109812630427361	68946170631612575387248983889883725676901012124357 366643041	59	195.457
8627	1429764598007 199774133443790513 617439464973514186509350238353	17635922425157317044560665997590419206477591941608 6210237623	60	196.812
8627	1429764598007 419109812630427361 617439464973514186509350238353	36998724588396798522622218959525938519002510639999 1338369031	60	197.881
8627	1429764598007 6675871535988671 199774133443790513 419109812630427361	79917077730957293127122644125679443275546661222956 7443071410521	63	208.958
8627	6675871535988671 199774133443790513 617439464973514186509350238353	82345830001055603843359532732545375034259271385580 8923910286719	63	209.001
8627	6675871535988671 419109812630427361 617439464973514186509350238353	17275482459970173412255705058640573679947665509272 12457233790543	64	210.070
8627	199774133443790513 419109812630427361 617439464973514186509350238353	51696539090949345725086971282527532801547264265964 175476425380129	65	214.973
8627	123348847 1429764598007 6675871535988671 617439464973514186509350238353	72694572943342998337738890429887190533519478717167 8569586528504727	66	218.787
8627	123348847 1429764598007 199774133443790513 617439464973514186509350238353	21753706969245988510600057723548829873656658973339 147285410393070681	68	223.690
8627	123348847 1429764598007 419109812630427361 617439464973514186509350238353	45637500184492946762567541252390641829118472775491 252397806834357257	68	224.759
8627	123348847 1429764598007 6675871535988671 199774133443790513 419109812630427361	98576793937229583134716025804938824196405839565513 243411596626429019287	71	235.836
8627	123348847 6675871535988671 199774133443790513 617439464973514186509350238353	10157263185888217516967166969018231385658466624471 4955016644598228062993	72	235.879
8627	123348847 6675871535988671 419109812630427361 617439464973514186509350238353	21309108428060445447917968881553821508400915609103 8437523824872918553921	72	236.948
8627	123348847 199774133443790513 419109812630427361 617439464973514186509350238353	63767084907590299305938568824218824168255348632109 82388322746320448861263	73	241.852
8627	1429764598007 6675871535988671 199774133443790513 617439464973514186509350238353	11773515252901202581475558651371909638174476100561 77825056394341323145969033	76	249.380
8627	1429764598007 6675871535988671 419109812630427361 617439464973514186509350238353	24699873234756234457983857630259596189410238653662 55812033953214929233247801	76	250.449
8627	1429764598007 199774133443790513 419109812630427361 617439464973514186509350238353	73913881431724352502628637430876131158913730800836 865282314541325471850802903	77	255.352
8627	6675871535988671 199774133443790513 419109812630427361 617439464973514186509350238353	34511945382639438225257002757175546006849596385271 1443701908326087198685012518559	81	267.541
8627	123348847 1429764598007 6675871535988671 199774133443790513 617439464973514186509350238353	14522495315822767433384337183276000220570088118333 5139947673951979534509692918254951	84	276.258
8627	123348847 1429764598007 6675871535988671 419109812630427361 617439464973514186509350238353	30467008845533418464539787833046735006493465479241 0887121436853913464107710318635447	84	277.327
8627	123348847 1429764598007 199774133443790513 419109812630427361 617439464973514186509350238353	91171920518979081030208068962796129782727824667516 13967667828163830804527494109302841	85	282.231
8627	123348847 6675871535988671 199774133443790513 419109812630427361 617439464973514186509350238353	42570086706755485218131775687734245765403518165385 634404335803722555979256210344818751473	89	294.420
8627	1429764598007 6675871535988671 199774133443790513 419109812630427361 617439464973514186509350238353	49343957716449016190758888061374785171214047244297 3980261427569786829899105662613271261911913	93	307.920
8627	123348847 1429764598007 6675871535988671 199774133443790513 419109812630427361 617439464973514186509350238353	60865202907407390814144408973726449857419503177876 11371624784930721750383980981451801705506948411431 1	101	334.798

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	100000000	100000000		-	skipped known factor: 123348847 skipped known factor: 1429764598007 skipped known factor: 6675871535988671 skipped known factor: 419109812630427361	-	-	0.018	-	-	26.298%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 123348847 skipped known factor: 1429764598007 skipped known factor: 6675871535988671 skipped known factor: 419109812630427361	-	-	0.071	-	-	29.984%

ECM factoring results:

Total ECM effort:	2,346.507 GHz-days
Estimated T-Level:	46.143

Digits	B1	Complete	FacMiss
20	11000	4,392.200	0.000%
25	50000	1,230.079	0.000%
30	250000	328.442	0.000%
35	1000000	67.467	0.000%
40	3000000	11.643	0.001%
45	11000000	1.741	17.540%
50	44000000	0.229	79.557%
55	110000000	0.027	97.336%
60	260000000	0.003	99.720%

ECM Summary

B1	B2	curves	GHz-days
3000000	300000000	2,711	20.69
3000000	600000000	1,000	10.12
11000000	36578884662	7,200	2,316

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.008
2013-04-18	Axon		3000000	300000000						30	0.229
2017-01-24	Ismo Laitela	6600K	3000000	600000000						1000	10.12
2017-12-08	James Hintz	10_12_2017	3000000	300000000						1000	7.633
2018-03-26	James Hintz	3_1_2018	3000000	300000000						1680	12.82
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

E553B4091A31B9__

2017-09-21

Oliver Kruse

Manual testing

E553B4091A31B9__

2017-10-02

kkmrkkblmbrbk

Manual testing

123348847

1429764598007

6675871535988671

199774133443790513

419109812630427361

617439464973514186509350238353

E553B4091A31B9__

2017-12-07

ATH

Manual testing

123348847

1429764598007

6675871535988671

199774133443790513

419109812630427361

617439464973514186509350238353

E553B4091A31B9__

2020-04-17

Oliver Kruse

Manual testing

123348847

1429764598007

6675871535988671

199774133443790513

419109812630427361

617439464973514186509350238353

C119ADB25F9B6B__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 400000000 (P-1 stage 1)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront