M1417543 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	20.9616	68.6567%	500000	15000000	0.0714	4.9146%	21.0330	70.1971%	1.5404%
PrimeNet	2⁵⁶	0.0068	62.5000%	6500	110000	0.0007	2.7688%	0.0074	63.5383%	1.0383%
GPU72	2⁶⁰	0.1083	65.0000%	6000	80000	0.0006	1.3012%	0.1089	65.4554%	0.4554%
Difference	+7	+20.8532	+3.6567%	+494000	+14920000	+0.0709	+3.6135%	+20.9241	+4.7417%	+4.7417%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1417543	6430485363481	13	42.548	2268180 2² × 3² × 5 × 12601	-	9	12601	8.052e-7	3.848e-5	7.099e-5
1417543	478693387204847	15	48.766	168846161 11 × 15349651	2008-08-26	11	15349651	4.730e-5	0.0463	0.0865
1417543	84621244298147214857	20	66.198	29847857983196 2² × 11 × 1031 × 657963539	2017-11-16	1031	657963539	10.820	1.9846	3.7067
1417543	225852582337280468201	21	67.614	79663397278700 2² × 5² × 796633972787	2019-01-25	25	796633972787	23.791	2,402.9	4,487.9
1417543	46871745708139085146793	23	75.311	16532742113692172 2² × 35895593 × 115144651	2021-10-20	35895593	115144651	6,907.6	2.2263	4.0444

exponent	prime factors	composite factor	digits	bits*
1417543	6430485363481 478693387204847	3078230820015911635399992407	28	91.314
1417543	6430485363481 84621244298147214857	544155672898785691664563448437217	33	108.746
1417543	6430485363481 225852582337280468201	1452341725024269472096549347167681	34	110.162
1417543	478693387204847 84621244298147214857	40507630062568936135256613180811879	35	114.964
1417543	478693387204847 225852582337280468201	108114137647994387626127378856570247	36	116.380
1417543	6430485363481 46871745708139085146793	301408074736991766690277992846466433	36	117.859
1417543	478693387204847 46871745708139085146793	22437194717233348629074900532956105671	38	124.077
1417543	84621244298147214857 225852582337280468201	19111926545330419188192505037793103262257	41	133.812
1417543	84621244298147214857 46871745708139085146793	3966345444249070748510757703392309955503601	43	141.509
1417543	225852582337280468201 46871745708139085146793	10586104806839555133360411004264147853629393	44	142.925
1417543	6430485363481 478693387204847 84621244298147214857	260483722226652488056345097589222091305997590799	48	157.512
1417543	6430485363481 478693387204847 225852582337280468201	695226379730798056144645726558897918944804949807	48	158.928
1417543	6430485363481 478693387204847 46871745708139085146793	14428205222674226287373150479844016379519868040075 1	51	166.625
1417543	6430485363481 84621244298147214857 225852582337280468201	12289896391767125325663017770135290727346967151343 6617	54	176.360
1417543	478693387204847 84621244298147214857 225852582337280468201	91487528539944482123569610239994136853273564184225 59679	55	182.578
1417543	6430485363481 84621244298147214857 46871745708139085146793	25505526325753194133333684489737419070956788612889 395081	56	184.057
1417543	6430485363481 225852582337280468201 46871745708139085146793	68073792016657617986595461985731091051482733230670 397033	56	185.473
1417543	478693387204847 84621244298147214857 46871745708139085146793	18986633355321013134253292065933894256206425708416 33154047	58	190.275
1417543	478693387204847 225852582337280468201 46871745708139085146793	50674983672915392237281941857467564917131322732965 11267871	58	191.691
1417543	84621244298147214857 225852582337280468201 46871745708139085146793	89580936102536052813505720700442524408021918392295 0022021491801	63	209.123
1417543	6430485363481 478693387204847 84621244298147214857 225852582337280468201	58830921321716325435594283186133419676623171294792 832002064729682599	68	225.126
1417543	6430485363481 478693387204847 84621244298147214857 46871745708139085146793	12209326789317192377005595588212777142383939556175 341664689583261157607	71	232.823
1417543	6430485363481 478693387204847 225852582337280468201 46871745708139085146793	32586474080332107646591765368479482248030717750830 148090464659592018951	71	234.239
1417543	6430485363481 84621244298147214857 225852582337280468201 46871745708139085146793	57604889845428478506236334708425801248546804024509 20463856669658347346319281	76	251.671
1417543	478693387204847 84621244298147214857 225852582337280468201 46871745708139085146793	42881801731903948428704135596659050776029731882855 3552242257040174456517959447	78	257.889
1417543	6430485363481 478693387204847 84621244298147214857 225852582337280468201 46871745708139085146793	27575079839670253712573459220608998693872598554878 60934512023985554071241542084146212755007	91	300.437

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:14:03	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 6430485363481	-	-	0.071	-	-	4.915%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:19:00	ANONYMOUS	Manual testing	?	?	478693387204847	48.766	15	2.08471e-5	0.117	4.49797e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.424 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.424 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		247	11.65
50000	5000000	84621244298147214857	1	0.047
50000	5000000	225852582337280468201	3	0.141
250000	35000000		43	11.69
250000	35000000	46871745708139085146793	7	1.902

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-17T04:11:49	ATH	ec2-1xe	50000	5000000	84621244298147214857	66.198	1	2		1	0.047
2017-12-24T22:46:42	Chang Chia-Tche	exbpc13	50000	5000000						3	0.141
2018-11-23T13:31:55	Chang Chia-Tche	exbpc13	50000	5000000						3	0.141
2019-01-25T12:26:35	TJAOI	Manual testing	50000	5000000	225852582337280468201	67.614	3	2		3	0.141
2019-01-25T12:26:35	TJAOI	Manual testing	50000	5000000						241	11.36
2021-10-20T13:16:17	TJAOI	Manual testing	250000	35000000	46871745708139085146793	75.311	7	2		7	1.902
2021-10-20T13:16:17	TJAOI	Manual testing	250000	35000000						43	11.69

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T19:29:09

Oliver Kruse

GTX-3

6430485363481

478693387204847

61F64C17BCCCBC__

2017-10-26T10:42:47

kkmrkkblmbrbk

c4.xlarge

6430485363481

478693387204847

61F64C17BCCCBC__

2017-11-17T15:27:10

kkmrkkblmbrbk

c4.xlarge

6430485363481

478693387204847

84621244298147214857

E780355E93900F__

2017-11-18T08:40:02

Oliver Kruse

GTX-2

6430485363481

478693387204847

84621244298147214857

E780355E93900F__

2019-01-25T13:16:43

ATH

ec2-PRPCF2

6430485363481

478693387204847

84621244298147214857

225852582337280468201

E780355E93900FDC

2021-10-21T06:26:30

SRJ2877

LTOS

6430485363481

478693387204847

84621244298147214857

225852582337280468201

46871745708139085146793

E780355E93900FDC

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