M4157 Mersenne number exponent details

is 2 ⁴¹⁵⁷ - 1

has 1252 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	7,147.9234	80.5970%	100000000000	100000000000	7.2057	16.0244%	7,155.1291	83.7062%	16.2062%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4128%	0.0000	68.2842%	0.7842%
GPU72	2⁴⁴	0.0006	70.4545%	500	10000	0.0000	0.9611%	0.0006	70.7385%	0.2840%
Difference	+23	+7,147.9228	+10.1425%	+99999999500	+99999990000	+7.2057	+15.0633%	+7,155.1285	+12.9677%	+12.9677%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4157	6118909921509137	16	52.442	735976656424 2³ × 19 × 53 × 91357579	-	53	91357579	0.2288	0.0004	0.0007
4157	4703418220474714722673	22	71.994	565722663035207448 2³ × 3 × 8731 × 31151 × 86667517	2009-10-25	31151	86667517	174,472	0.0003	0.0006
4157	50476826913711066101626583	26	85.384	6071304656448287960263 7 × 103 × 12433 × 8879701 × 76273291	-	8879701	76273291	2.710e+9	0.0009	0.0013
4157	99113662466478772809979281191	29	96.323	11921296904796580804664335 5 × 438001 × 8448197 × 644338921111	-	8448197	644338921111	7.416e+12	2.5302	4.7246
4157	41161769340018076868666055145622172588108913	44	144.884	4950898405102005877876600330240819411608 2³ × 3 × 7 × 29469633363702415939741668632385829831	2020-09-30	8	29469633363702415939741668632385829831	3.144e+13	1.157e+26	2.161e+26

exponent	prime factors	composite factor	digits	bits*
4157	6118909921509137 4703418220474714722673	28779792414269581488726418168590563201	38	124.436
4157	6118909921509137 50476826913711066101626583	308863157008606073521095804017813796588871	42	137.826
4157	6118909921509137 99113662466478772809979281191	606467572623244725650082874436213017198742167	45	148.765
4157	4703418220474714722673 50476826913711066101626583	237413627417697089007770213364227094583049616359	48	157.378
4157	4703418220474714722673 99113662466478772809979281191	46617300594281711406857694876958338741746145014354 3	51	168.317
4157	50476826913711066101626583 99113662466478772809979281191	50029431851044300453059468559447539436538622542375 00353	55	181.707
4157	6118909921509137 41161769340018076868666055145622172588108913	25186515880150721262749012246916264088563051046921 7880638081	60	197.326
4157	6118909921509137 4703418220474714722673 50476826913711066101626583	14527126003076203909250292474488050586628501462290 59130163172183	64	209.820
4157	4703418220474714722673 41161769340018076868666055145622172588108913	19360101590081849579042114646895968239879897103879 8725292314484449	66	216.878
4157	6118909921509137 4703418220474714722673 99113662466478772809979281191	28524706312032415236895122431836455942711908130379 36207131836052391	67	220.759
4157	50476826913711066101626583 41161769340018076868666055145622172588108913	20777155064381914492514447608909806229870347718062 60630497033260034279	70	230.268
4157	6118909921509137 50476826913711066101626583 99113662466478772809979281191	30612558692082019909707551897116046598122636926031 361666748420330225361	71	234.149
4157	99113662466478772809979281191 41161769340018076868666055145622172588108913	40796937128896063930700490786510878490459197250151 27721883037465760355383	73	241.207
4157	4703418220474714722673 50476826913711066101626583 99113662466478772809979281191	23530934132819979664473040730103412399155919249721 797655882329259151134603569	77	253.701
4157	6118909921509137 4703418220474714722673 41161769340018076868666055145622172588108913	11846271770097664863449997163883591704287868281913 74507831077590546139438197910513	82	269.321
4157	6118909921509137 50476826913711066101626583 41161769340018076868666055145622172588108913	12713354026418030871923454850896826964639878921023 049184473136094520090596096031707223	86	282.710
4157	6118909921509137 99113662466478772809979281191 41161769340018076868666055145622172588108913	24963278336518661154240824485463556314726807504164 349323547273833792100407729284801634471	89	293.649
4157	4703418220474714722673 50476826913711066101626583 41161769340018076868666055145622172588108913	97723649699442391066896484495452612489351108323154 15540121050745682782943349809849958507767	91	302.262
4157	6118909921509137 4703418220474714722673 50476826913711066101626583 99113662466478772809979281191	14398366632769017448754390614689766402335222740166 6631425578535405531419036201187326706309953	93	306.143
4157	4703418220474714722673 99113662466478772809979281191 41161769340018076868666055145622172588108913	19188505743161114227299321757172115789457538784483 135372634547902623262065978574098718767698759	95	313.201
4157	50476826913711066101626583 99113662466478772809979281191 41161769340018076868666055145622172588108913	20592999340648391088395000261453458633627244408655 9151610622323144155160207234598845972692439946289	99	326.591
4157	6118909921509137 4703418220474714722673 50476826913711066101626583 41161769340018076868666055145622172588108913	59796220971200144070421967431987414537302026033588 43907351684467055343988445742752380292675143018117 5967079	107	354.704
4157	6118909921509137 4703418220474714722673 99113662466478772809979281191 41161769340018076868666055145622172588108913	11741273817076359799539188915087610699015382079331 31808129149571629282559963971534045700343417301617 17882060983	111	365.644
4157	6118909921509137 50476826913711066101626583 99113662466478772809979281191 41161769340018076868666055145622172588108913	12600670797912455670876785496017732716118047959636 55318908478528844416340694037928655508260618511043 180030102742593	115	379.033
4157	4703418220474714722673 50476826913711066101626583 99113662466478772809979281191 41161769340018076868666055145622172588108913	96857488313029429229843847618156038197214327147224 39192082662066785938044380467943051981930439159640 38545806289650510497	120	398.585
4157	6118909921509137 4703418220474714722673 50476826913711066101626583 99113662466478772809979281191 41161769340018076868666055145622172588108913	59266224621105105910668977298134220889575481176410 60702182946409548623119974817573346497355999856273 457537402701379804479701732699911089	136	451.028

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2019-02-10T02:54:05	Jocelyn Larouche	Manual testing	1000000000	1000000000		-		-	-	0.072	-	-	8.434%
2019-02-11T00:22:42	Jocelyn Larouche	Manual testing	10000000000	10000000000		-		-	-	0.721	-	-	12.117%
2019-02-11T11:43:23	Jocelyn Larouche	Manual testing	20000000000	20000000000		-		-	-	1.441	-	-	13.278%
2019-02-16T19:25:00	Jocelyn Larouche	Manual testing	100000000000	100000000000		-		-	-	7.206	-	-	16.024%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	4703418220474714722673	71.994	22	59,466	4.86484e-7	140,040

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.654 GHz-days
Estimated T-Level:	38.404

Digits	B1	Curves	Complete	FacMiss
20	11000	3287 / 100	32.870	0.000%
25	50000	3287 / 280	11.739	0.001%
30	250000	3287 / 640	5.136	0.586%
35	1000000	3200 / 1580	2.025	13.187%
40	3000000	3200 / 4700	0.681	50.615%
45	11000000	232 / 9700	0.024	97.637%

New Calculation Method

Total ECM effort:	15.654 GHz-days
Estimated T-Level:	38.404

Digits	B1	Complete	FacMiss
20	11000	660.550	0.000%
25	50000	162.684	0.000%
30	250000	32.446	0.000%
35	1000000	5.278	0.510%
40	3000000	0.719	48.715%
45	11000000	0.085	91.818%
50	44000000	0.009	99.091%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		2,968	9.232
11000000	11000000		87	0.673
11000000	1100000000		231	2.635
110000000	900514153782	41161769340018076868666055145622172588108913	1	3.114

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13T13:00:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2010-05-30T09:51:00	James Hintz	18_051310	3000000	300000000						100	0.311
2010-05-30T11:59:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-05-30T12:12:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-05-31T02:07:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-05-31T15:10:00	James Hintz	18_051310	3000000	300000000						100	0.311
2010-06-01T05:17:00	James Hintz	13_052010	3000000	300000000						100	0.311
2010-06-01T21:19:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-02T14:19:00	James Hintz	18_051310	3000000	300000000						100	0.311
2010-06-02T20:48:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-06-02T21:18:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-06-03T06:18:00	James Hintz	13_052010	3000000	300000000						100	0.311
2010-06-03T11:01:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-08T15:15:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-08-18T11:46:00	James Hintz	NEW_OMFG	3000000	300000000						1667	5.185
2010-12-30T08:55:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-01T22:58:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-13T22:53:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-24T08:26:00	James Hintz	OMFG	11000000	1100000000						11	0.125
2011-03-17T17:02:00	James Hintz	13_052010	11000000	1100000000						11	0.125
2016-10-01T18:17:57	kkmrkkblmbrbk	kel1	11000000	11000000						87	0.673
2020-03-09T19:35:34	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-05-17T00:13:03	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-09-30T15:28:19	Ryan Propper	Manual testing	110000000	900514153782	41161769340018076868666055145622172588108913	144.884	1	2	15512902750274620828	1	3.114

Lucas-Lehmer results:
Exponent "4157" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:11

Oliver Kruse

Oliver-PC

08B5F23BC47A87__

2017-09-21T19:21:10

Oliver Kruse

Manual testing

08B5F23BC47A87__

2017-10-02T09:55:57

kkmrkkblmbrbk

Manual testing

6118909921509137

4703418220474714722673

50476826913711066101626583

99113662466478772809979281191

08B5F23BC47A87__

2017-12-07T02:44:27

ATH

Manual testing

6118909921509137

4703418220474714722673

50476826913711066101626583

99113662466478772809979281191

08B5F23BC47A87__

2020-04-17T12:32:17

Oliver Kruse

IOS-1

6118909921509137

4703418220474714722673

50476826913711066101626583

99113662466478772809979281191

8C77BD58CCE589__

2020-10-01T09:32:44

Yuji Hasegawa

vj22m

6118909921509137

4703418220474714722673

50476826913711066101626583

99113662466478772809979281191

41161769340018076868666055145622172588108913

8C77BD58CCE589A7

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 = 100000000000 (P-1 stage 1)

B1 = 20000000000 (P-1 stage 1)

B1 = 10000000000 (P-1 stage 1)

B1 = 1000000000 (P-1 stage 1)

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TF factor-bounds graph:

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Last modified: 2020-10-01T09:32:44+00:00

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