M2827553 Mersenne number exponent details

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M2827553

<<<

>>>

is 2 ^2827553 - 1

has 851179 decimal digits

takes 0.218 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	C304EF20EF8337E8	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	2⁶⁸	21.0800	67.6471%	5000000	200000000	1.7498	9.1667%	22.8298	70.6128%	2.9657%
PrimeNet	2⁵⁹	0.0272	62.7119%	12000	240000	0.0027	2.9323%	0.0299	63.8053%	1.0934%
GPU72	2⁶³	0.5645	65.0794%	16000	260000	0.0033	1.8262%	0.5677	65.7171%	0.6377%
Difference	+5	+20.5156	+2.5677%	+4984000	+199740000	+1.7465	+7.3405%	+22.2621	+4.8957%	+4.8957%

Known prime factors (1 factor, 69.4 bits, 0.00245498% 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
2827553	787454155878949450769	21	69.416	139246577496328 2³ × 17405822187041	2020-09-13	8	17405822187041	43.577	106,204	198,360

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.243%
2016-09-19T01:31:06	Jocelyn Larouche	low 4M	120000	3300000	6	-		-	-	0.033	-	-	2.866%
2016-09-21T12:09:20	Jocelyn Larouche	low 4M	120000	3630000		-		-	-	0.035	-	-	2.927%
2016-09-22T12:02:47	Jocelyn Larouche	low 4M	120000	3993000		-		-	-	0.037	-	-	2.987%
2016-12-24T02:28:32	Jocelyn Larouche	low 4M	207360	207360		-		-	-	0.023	-	-	1.255%
2017-02-25T21:08:07	Jocelyn Larouche	low 4M	298598	2985980	6	-		-	-	0.050	-	-	3.228%
2017-10-07T21:35:20	Jocelyn Larouche	low 4M	597196	5971960	6	-		-	-	0.100	-	-	4.096%
2019-11-10T16:24:54	masser	Manual testing	3000000	30000000	12	-		-	-	0.501	-	-	6.483%
2020-01-24T15:13:23	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.167%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-13T15:00:00	Sturle Sunde	gigi.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-15T10:38:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.347	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.694	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.321	-	-
2016-02-13T14:46:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.643	-	-
2017-10-28T16:39:39	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.286	-	-
2019-01-03T01:11:02	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.57	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.548 GHz-days
Estimated T-Level:	1.700

Digits	B1	Curves	Complete	FacMiss
20	11000	34 / 100	0.340	71.055%
25	50000	34 / 280	0.121	88.546%

New Calculation Method

Total ECM effort:	3.548 GHz-days
Estimated T-Level:	1.700

Digits	B1	Complete	FacMiss
20	11000	1.308	27.044%
25	50000	0.121	88.604%
30	250000	0.008	99.240%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	3.130
50000	5000000	787454155878949450769	4	0.417

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-20T02:43:00	James Hintz	4115	50000	5000000						3	0.313
2010-10-29T07:25:00	Mistel		50000	5000000						3	0.313
2013-04-03T18:21:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-03-31T05:33:00	Bruce	desk16	50000	5000000						3	0.313
2016-02-17T09:20:49	Sintax	cloud2	50000	5000000						3	0.313
2016-06-09T15:31:54	lettp	Home	50000	5000000						3	0.313
2017-02-26T23:01:22	Bruce	eleven	50000	5000000						3	0.313
2017-09-22T06:35:49	Sebastian Hornbostel	V2	50000	5000000						3	0.313
2018-03-08T05:07:05	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2019-01-15T15:19:28	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-09-13T13:49:35	rextherunt	ice	50000	5000000	787454155878949450769	69.416	4	2		4	0.417

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	C304EF20EF8337E8	0.218
2018-09-09T05:26:56	kkmrkkblmbrbk	old	C304EF20EF8337E8	0.218

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-13T16:34:12

bald2718281828

splint1

787454155878949450769

1179F6527B34D644

2020-09-14T21:59:45

oodaira

com1

787454155878949450769

1179F6527B34D644

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 3000000, B2 = 30000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 597196, B2 = 5971960 (P-1 stage 2)

B1 = 597196 (P-1 stage 1)

B1 = 298598, B2 = 2985980 (P-1 stage 2)

B1 = 120000, B2 = 3993000 (P-1 stage 2)

B1 = 120000, B2 = 3630000 (P-1 stage 2)

B1 = 298598 (P-1 stage 1)

B1 = 120000, B2 = 3300000 (P-1 stage 2)

B1 = 207360 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

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10³

10⁴

10⁵

10⁶

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10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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10¹⁴

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-09-14T21:59:45+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