M285151 Mersenne number exponent details

is 2 ²⁸⁵¹⁵¹ - 1

has 85840 decimal digits

takes 0.002 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	104.2041	71.6418%	50000	50000	0.0005	0.3947%	104.2046	71.7537%	0.1119%
PrimeNet	2⁴⁰	0.0000	52.5000%	3000	80000	0.0001	15.0495%	0.0001	59.6485%	7.1485%
GPU72	2⁴⁴	0.0000	56.8182%	5000	130000	0.0001	10.8685%	0.0001	61.5114%	4.6932%
Difference	+23	+104.2041	+14.8236%	+45000	-80000	+0.0004	-10.4738%	+104.2045	+10.2423%	+10.2423%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
285151	88967113	8	26.407	156 2² × 3 × 13	-	4	13	3.241e-11	4.449e-8	8.066e-8
285151	2292614041	10	31.094	4020 2² × 3 × 5 × 67	2008-07-21	5	67	1.876e-9	8.301e-8	1.008e-7
285151	52322356991	11	35.607	91745 5 × 59 × 311	2008-07-21	59	311	2.983e-8	7.206e-7	1.190e-6
285151	5991861038717849	16	52.412	10506470324 2² × 7 × 109 × 3442487	2014-08-08	109	3442487	0.0037	0.0019	0.0035
285151	37913160706323198540170777	26	84.971	66479094771407427188 2² × 16619773692851856797	2020-07-05	4	16619773692851856797	17,867,460	8.972e+9	1.676e+10

exponent	prime factors	composite factor	digits	bits*
285151	88967113 2292614041	203967252451033633	18	57.501
285151	88967113 52322356991	4654969046844636983	19	62.013
285151	2292614041 52322356991	119954970295781110631	21	66.701
285151	88967113 5991861038717849	533078578111908247099937	24	78.819
285151	2292614041 5991861038717849	13737024749085385254717809	26	83.506
285151	52322356991 5991861038717849	313508292308259368301632359	27	88.019
285151	88967113 2292614041 52322356991	10672047397216401492773678303	29	93.108
285151	88967113 2292614041 5991861038717849	1222143433135676116605013096415417	34	109.913
285151	88967113 37913160706323198540170777	3373024452746615819044808556656801	34	111.378
285151	88967113 52322356991 5991861038717849	27891927668225942052999944167609567	35	114.425
285151	2292614041 37913160706323198540170777	86920244574006042457226225888079857	35	116.065
285151	2292614041 52322356991 5991861038717849	718753512915847728038112669463352719	36	119.113
285151	52322356991 37913160706323198540170777	1983705929133396105043785448299852007	37	120.578
285151	5991861038717849 37913160706323198540170777	227170390490866458068261158321349578098673	42	137.383
285151	88967113 2292614041 37913160706323198540170777	7733043221003232441974843305148325990742841	43	142.472
285151	88967113 2292614041 52322356991 5991861038717849	63945425002731184311160038170877750710130247	44	145.520
285151	88967113 52322356991 37913160706323198540170777	176484589555980843351190329926648591390045791	45	146.984
285151	2292614041 52322356991 37913160706323198540170777	4547872066346174872438093438563720289470230287	46	151.672
285151	88967113 5991861038717849 37913160706323198540170777	20210693801055041642868752185886398227206965941049	50	163.790
285151	2292614041 5991861038717849 37913160706323198540170777	52081402693881332402323326802245003281844380326759 3	51	168.477
285151	52322356991 5991861038717849 37913160706323198540170777	11886090269047986543955292572308822922186003729372 943	53	172.990
285151	88967113 2292614041 52322356991 37913160706323198540170777	40461104803616363699396044445325706069369068807955 1431	54	178.079
285151	88967113 2292614041 5991861038717849 37913160706323198540170777	46335320386650449084280608781512598606612198329457 715669009	59	194.884
285151	88967113 52322356991 5991861038717849 37913160706323198540170777	10574711360945926212785499812286597198151124008095 44039023559	61	199.396
285151	2292614041 52322356991 5991861038717849 37913160706323198540170777	27250217443412881653450967427538215219586282563638 773247292663	62	204.084
285151	88967113 2292614041 52322356991 5991861038717849 37913160706323198540170777	24243731745626849477181990590851117052592526140891 80430673263293191919	70	230.491

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-02-06T16:48:00	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 88967113 skipped known factor: 2292614041 skipped known factor: 52322356991	-	-	0.000	-	-	0.395%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-21T09:15:00	J Feitsma	Manual testing	?	?	2292614041	31.094	10	8.72977e-10	0.004	1.81522e-9
2008-07-21T09:15:00	J Feitsma	Manual testing	?	?	52322356991	35.607	11	1.37765e-8	0.004	2.86459e-8
2014-08-08T10:34:00	TJAOI	Manual testing	?	?	5991861038717849	52.412	16	0.002	0.004	0.003

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.727 GHz-days
Estimated T-Level:	26.398

Digits	B1	Curves	Complete	FacMiss
20	11000	460 / 100	4.600	0.982%
25	50000	460 / 280	1.643	19.286%
30	250000	179 / 640	0.280	75.585%

New Calculation Method

Total ECM effort:	8.727 GHz-days
Estimated T-Level:	26.398

Digits	B1	Complete	FacMiss
20	11000	23.981	0.000%
25	50000	2.990	5.029%
30	250000	0.285	75.207%
35	1000000	0.022	97.843%
40	3000000	0.001	99.861%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	2.055
250000	25000000		157	5.742
250000	25000000	37913160706323198540170777	1	0.037
250000	36750000		14	0.592
250000	38250000		7	0.301

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-08-22T10:13:00	TJAOI	Manual testing	50000	5000000						50	0.366
2015-01-23T13:31:00	TJAOI	Manual testing	50000	5000000						50	0.366
2015-10-09T10:36:10	TJAOI	Manual testing	50000	5000000						90	0.658
2016-03-04T13:12:07	TJAOI	Manual testing	50000	5000000						91	0.666
2018-10-26T10:41:38	TJAOI	Manual testing	250000	25000000						44	1.609
2020-04-13T01:28:34	Oliver Kruse	Melissa	250000	25000000						3	0.110
2020-04-29T12:46:29	Greg	azure3	250000	25000000						3	0.110
2020-05-03T17:22:59	MarkS	desktop-i7	250000	25000000						3	0.110
2020-05-09T19:12:20	Greg Hogan	azure2	250000	25000000						3	0.110
2020-05-29T19:50:27	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.110
2020-06-15T21:11:31	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						3	0.110
2020-06-26T04:45:16	nordi	sweet16	250000	25000000						3	0.110
2020-07-05T14:51:33	MarkS	desktop-i7	250000	25000000	37913160706323198540170777	84.971	1	2	3682103276756178	1	0.037
2020-07-12T19:43:24	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.110
2020-07-24T05:14:39	Ahmed Azhad	c5.4xlarge.azf	250000	25000000						3	0.110
2020-08-08T17:44:02	Ahmed Azhad	c5.xlarge.az	250000	25000000						3	0.110
2020-09-20T20:55:22	MarkS	desktop-i7	250000	25000000						7	0.256
2020-10-26T00:23:57	Tsurumaki Kokoro	Baidu_HK_1	250000	25000000						7	0.256
2020-11-09T15:10:39	nordi	sweet16	250000	25000000						7	0.256
2021-01-09T19:01:27	zampel	goldammer	250000	25000000						7	0.256
2021-01-30T22:33:42	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						7	0.256
2021-02-12T10:22:48	TJAOI	Manual testing	250000	25000000						48	1.755
2022-01-21T04:05:27	Klaus Nordmann	no1	250000	36750000						7	0.296
2022-03-24T05:47:52	Eric	miniPCWindows	250000	38250000						7	0.301
2022-05-19T10:12:11	debrouxl	dl380g9-1	250000	36750000						7	0.296

Lucas-Lehmer results:
No L-L results for M285151

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T12:16:13

Oliver Kruse

Ollaptop

01C18406F769F0__

2017-09-22T20:36:20

Oliver Kruse

Manual testing

01C18406F769F0__

2017-10-12T19:35:52

Oliver Kruse

GTX-1

01C18406F769F0__

2017-11-06T19:44:48

kkmrkkblmbrbk

c4.xlarge

88967113

2292614041

52322356991

5991861038717849

01C18406F769F0__

2020-04-17T22:12:32

Oliver Kruse

AddPrpType5

88967113

2292614041

52322356991

5991861038717849

BD46ABC8D4043D__

2020-07-05T15:57:45

riccardo uberti

Colab_noGPU12

88967113

2292614041

52322356991

5991861038717849

37913160706323198540170777

BD46ABC8D4043DDD

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 = 50000 (P-1 stage 1)

10⁰

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10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-19T10:12:11+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