M1450487 Mersenne number exponent details

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M1450487

<<<

>>>

is 2 ^1450487 - 1

has 436641 decimal digits

takes 0.055 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	009BDE797ACDBC46	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	20.4855	68.6567%	500000	15000000	0.0714	4.9283%	20.5569	70.2014%	1.5447%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9043%	0.0073	63.5891%	1.0891%
GPU72	2⁶⁰	0.1059	65.0000%	6500	90000	0.0006	1.3966%	0.1065	65.4888%	0.4888%
Difference	+7	+20.3796	+3.6567%	+493500	+14910000	+0.0708	+3.5318%	+20.4504	+4.7126%	+4.7126%

Known prime factors (4 factors, 321.7 bits, 0.02217988% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1450487	37369203710805008218607	23	74.984	12881605871271169 683 × 126311 × 149316613	2022-01-18	126311	149316613	2,699.9	0.4570	0.8412
1450487	253763650749713532283313	24	77.748	87475327510592488 2³ × 37 × 2677 × 110394006389	2014-10-26	2677	110394006389	27,807	332.98	621.91
1450487	1578948245746208619195007	25	80.385	544282108611179769 3² × 23 × 23059 × 315551 × 361363	2015-02-03	315551	361363	182,300	0.0176	0.0356
1450487	468763503576730222318832041	27	88.599	161588316054101216460 2² × 3 × 5 × 3877 × 12575231 × 55239143	2022-01-18	12575231	55239143	44,900,914	0.8249	1.4169

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1450487	37369203710805008218607 253763650749713532283313	9482945559263621036476020721330181383362204991	46	152.732
1450487	37369203710805008218607 1578948245746208619195007	59004038644108277165436835863838331811418895249	47	155.370
1450487	253763650749713532283313 1578948245746208619195007	400679671185413739479315641948177297264719018191	48	158.133
1450487	37369203710805008218607 468763503576730222318832041	17517318857349503766508302778610774164114243986887	50	163.583
1450487	253763650749713532283313 468763503576730222318832041	11895513800585745835295012493574061904869407403183 3	51	166.347
1450487	1578948245746208619195007 468763503576730222318832041	74015331164232477410178526586080411047128985881928 7	51	168.984
1450487	37369203710805008218607 253763650749713532283313 1578948245746208619195007	14973080255306093639568423977771364957330683635772 346039154330937679937	71	233.117
1450487	37369203710805008218607 253763650749713532283313 468763503576730222318832041	44452587845878103981544794530739149252897939080519 89029226513261540916631	73	241.331
1450487	37369203710805008218607 1578948245746208619195007 468763503576730222318832041	27658939879988978640290605454572719153976020650070 152264420428756203873209	74	243.968
1450487	253763650749713532283313 1578948245746208619195007 468763503576730222318832041	18782400647684678286405358284533156090735929383033 7859118691550263352657831	75	246.732
1450487	37369203710805008218607 253763650749713532283313 1578948245746208619195007 468763503576730222318832041	70188335598128466961705116325664272302206981435599 49661214531376109017633910770477805952118461417	97	321.716

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.839%
2010-07-23T13:54:00	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.216%
2010-07-24T14:59:00	Rob_Dee	twopc	200000	300000		-		-	-	0.011	-	-	1.519%
2010-07-25T15:20:00	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.333%
2010-07-26T14:46:00	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.820%
2010-07-27T14:03:00	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	3.111%
2010-07-28T13:48:00	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	3.321%
2010-07-29T14:25:00	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.485%
2015-02-03T11:40:00	alpertron	Manual testing	500000	15000000	12		1578948245746208619195007	25	80.385	0.028	0.111	0.055	4.928%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2010-05-07T00:30:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.106	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.100	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.532 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:	25.532 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	11.84
50000	5000000	253763650749713532283313	1	0.047
250000	35000000		20	5.460
250000	35000000	37369203710805008218607	12	3.276
250000	35000000	468763503576730222318832041	18	4.914

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-05T05:00:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-12-16T18:32:00	Johan Koolwaaij	C0B5A3B75	50000	5000000						3	0.142
2009-06-29T10:00:00	James Hintz	06_060209	50000	5000000						3	0.142
2010-04-16T21:59:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.142
2011-07-15T00:31:00	S36049	Wolle5	50000	5000000						3	0.142
2012-11-20T14:58:00	Donna Noble	CCI-i7-3770s-XP	50000	5000000						3	0.142
2013-08-24T00:00:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2014-02-16T23:04:00	Bruce	snowflake	50000	5000000						3	0.142
2014-10-26T12:40:00	Chang Chia-Tche	exbpc13	50000	5000000	253763650749713532283313	77.748	1	2		1	0.047
2019-03-29T12:18:30	TJAOI	Manual testing	50000	5000000						228	10.79
2022-01-18T14:04:48	TJAOI	Manual testing	250000	35000000	37369203710805008218607	74.984	12	2		12	3.276
2022-01-18T14:04:48	TJAOI	Manual testing	250000	35000000	468763503576730222318832041	88.599	18	2		18	4.914
2022-01-18T14:04:48	TJAOI	Manual testing	250000	35000000						20	5.460

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	009BDE797ACDBC46	0.055

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T01:36:37

Oliver Kruse

GTX-1

253763650749713532283313

1578948245746208619195007

159DBD32F6867352

2017-10-05T21:17:54

Oliver Kruse

Manual testing

253763650749713532283313

1578948245746208619195007

159DBD32F68673__

2017-10-27T12:50:14

kkmrkkblmbrbk

c4.xlarge

253763650749713532283313

1578948245746208619195007

159DBD32F68673__

2022-01-18T20:06:28

SRJ2877

LTOS

37369203710805008218607

253763650749713532283313

1578948245746208619195007

468763503576730222318832041

DF7E6E1CAA3C3D60

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 200000, B2 = 4000000 (P-1 stage 2)

B1 = 200000, B2 = 3000000 (P-1 stage 2)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 200000, B2 = 1000000 (P-1 stage 2)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶¹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-18T20:06:28+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