M898 727 Mersenne number exponent details

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M898727

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is 2 ⁸⁹⁸⁷²⁷ - 1

has 270544 decimal digits

takes 0.022 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	DA0C1E7456C9C0A0	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	66.3214	70.5882%	1000000	10002962970	19.1964	11.0687%	85.5179	73.8437%
Target	2⁴⁴	0.0000	54.5455%	15000	600000	0.0016	17.9840%	0.0017	62.7200%
Difference	+24	+66.3214	+16.0428%	+985000	+10002362970	+19.1948	-6.9153%	+85.5162	+11.1237%

Known prime factors (1 factor, 86.5 bits, 0.00962911% 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
898727	112452995398776104186479111	27	86.539	62562377339712784965 3 × 5 × 281 × 14842794149398051	2023-03-09	281	14842794149398051	19,645,394	28,435,083	53,108,816

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.169%
2002-02-17	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.370%
2002-04-20	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.680%
2002-05-25	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.120%
2002-07-14	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.702%
2002-12-16	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.015	-	-	2.421%
2003-08-25	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.266%
2011-06-07	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.007	-	-	1.012%
2011-07-12	Jocelyn Larouche	Manual testing	228932	228932		-		-	-	0.008	-	-	1.088%
2011-09-11	Jocelyn Larouche	Manual testing	381554	381554		-		-	-	0.013	-	-	1.404%
2011-10-15	Jocelyn Larouche	Manual testing	763108	763108		-		-	-	0.027	-	-	1.912%
2013-10-11	David Campeau	i5-2500k	990000	25740000		-		-	-	0.082	-	-	5.066%
2015-04-27	Sid & Andy	Speck	8987270	269618100		-		-	-	0.815	-	-	8.944%
2023-01-12	Jocelyn Larouche	Manual testing	1850188	3470356890		-		-	-	6.710	-	-	10.693%
2023-03-07	Jocelyn Larouche	Manual testing	1000000	3470356890		-		-	-	6.682	-	-	9.961%
2023-03-09	Jocelyn Larouche	Manual testing	1000000	10002962970		-		-	-	19.20	-	-	11.069%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2023-03-09	masser	Manual testing	5000000	230000000	2	7			-	-	0.690
2023-03-09	masser	Manual testing	5000000	5000000	6	5	112452995398776104186479111	P+1	27	86.539	0.267
2023-03-09	masser	Manual testing	5000000	220000000	127	17			-	-	0.671

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-01	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.021	-	-
2003-08-25	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.043	-	-
2008-10-13	Sturle Sunde	gehry.ifi	2⁵⁸	2⁵⁹		-	-	0.043	-	-
2008-10-13	Sturle Sunde	gehry.ifi	2⁵⁹	2⁶⁰		-	-	0.085	-	-
2010-05-27	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.171	-	-
2014-06-05	lycorn	Manual testing	2⁶¹	2⁶²		-	-	0.342	-	-
2015-10-11	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.092	-	-
2015-10-11	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.185	-	-
2016-01-17	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	4.157	-	-
2018-05-11	BloodERazor	Manual testing	2⁶⁵	2⁶⁶		-	-	8.315	-	-
2019-02-10	lycorn	Manual testing	2⁶⁶	2⁶⁷		-	-	16.63	-	-
2022-03-02	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	33.26	-	-

ECM factoring results:

Total ECM effort:	13.986 GHz-days
Estimated T-Level:	25.652

Digits	B1	Complete	FacMiss
20	11000	14.794	0.000%
25	50000	1.613	19.934%
30	250000	0.130	87.775%
35	1000000	0.009	99.140%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		283	7.948
250000	25000000		43	6.038

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-08	Team_Bundu	bundu1	50000	5000000						1	0.028
2008-01-28	Steve Scott	Abit-2	50000	5000000						3	0.084
2008-10-25	Sturle Sunde	v21	50000	5000000						3	0.084
2010-05-28	James Hintz	13_052010	50000	5000000						3	0.084
2010-05-28	unconnected	xp-lm	50000	5000000						3	0.084
2010-05-29	Lupo	yorick	50000	5000000						3	0.084
2010-06-02	James Hintz	14_052810	50000	5000000						3	0.084
2010-06-03	James Hintz	terri_castor	50000	5000000						3	0.084
2010-08-13	unconnected	xp-lm	50000	5000000						3	0.084
2011-01-16	arnaud	Arnaud-PC	50000	5000000						3	0.084
2011-10-05	Andriy Makukha	freehost	50000	5000000						3	0.084
2012-02-01	Pool Party	sts	50000	5000000						3	0.084
2012-10-02	Pool Party	sts	50000	5000000						3	0.084
2012-12-22	gucs	echo3	50000	5000000						3	0.084
2013-03-17	gucs	echo3	50000	5000000						3	0.084
2013-06-02	gucs	echo3	50000	5000000						3	0.084
2013-08-19	gucs	echo3	50000	5000000						3	0.084
2013-11-02	gucs	echo3	50000	5000000						3	0.084
2014-01-24	Ryan Schulz	wenn	50000	5000000						15	0.421
2015-02-22	Bruce	desk16	50000	5000000						3	0.084
2015-02-26	Bruce	desk16	50000	5000000						3	0.084
2015-06-11	westicles	Manual testing	50000	5000000						207	5.813
2015-06-11	guru	h1	50000	5000000						3	0.084
2019-06-30	storm5510	7700_Kaby_Lake	250000	25000000						3	0.421
2020-01-06	TJAOI	Manual testing	250000	25000000						40	5.617

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	tom ehlert		DA0C1E7456C9C0A0	0.022
2002-02-03	ANONYMOUS	v4_computers	DA0C1E7456C9C0A0	0.022
2015-04-11	MadPoo	Manual testing	DA0C1E7456C9C0A0	0.022

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-03-15

Oliver Kruse

Server-Phi

112452995398776104186479111

00F551E1CB121A34

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 = 1000000, B2 = 10002962970 (P-1 stage 2)

B1 = 1850188, B2 = 3470356890 (P-1 stage 2)

B1 = 1000000, B2 = 3470356890 (P-1 stage 2)

B1 = 8987270, B2 = 269618100 (P-1 stage 2)

B1 = 8987270 (P-1 stage 1)

B1 = 5000000 (P+1 stage 1)

B1 = 990000, B2 = 25740000 (P-1 stage 2)

B1 = 1850188 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 990000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 763108 (P-1 stage 1)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 381554 (P-1 stage 1)

B1 = 228932 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

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10⁴

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10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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10¹⁷

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=25.65 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-03-25T13:08:14+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