M932 567 Mersenne number exponent details

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M932567

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is 2 ⁹³²⁵⁶⁷ - 1

has 280731 decimal digits

takes 0.023 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	30A086AD77F7E071	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	63.9148	70.5882%	50000000	1263691439010	2,422.5792	21.8857%	2,486.4941	77.0252%
Target	2⁴⁴	0.0000	54.5455%	15000	600000	0.0016	18.0559%	0.0017	62.7527%
Difference	+24	+63.9148	+16.0428%	+49985000	+1263690839010	+2,422.5776	+3.8298%	+2,486.4924	+14.2725%

Known prime factors (1 factor, 105.0 bits, 0.01126043% 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
932567	40875951889311160318482553348879	32	105.011	21915825827694503621982417 3³ × 11 × 41941 × 1759391987613713221	2022-11-11	41941	1759391987613713221	1.716e+11	3.371e+9	6.295e+9

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	-	-	0.171%
2002-02-24	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.373%
2002-04-28	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.685%
2002-05-25	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.129%
2002-07-27	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.713%
2002-12-31	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.015	-	-	2.435%
2003-09-09	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.283%
2011-06-01	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.007	-	-	1.019%
2011-07-14	Jocelyn Larouche	Manual testing	218219	218219		-		-	-	0.008	-	-	1.067%
2011-09-18	Jocelyn Larouche	Manual testing	363699	363699		-		-	-	0.013	-	-	1.380%
2012-01-09	Jocelyn Larouche	Manual testing	727399	727399		-		-	-	0.026	-	-	1.884%
2013-10-17	David Campeau	i5-2500k	870000	26100000		-		-	-	0.079	-	-	5.028%
2014-08-01	alpertron	Manual testing	10000000	500000000		-		-	-	1.290	-	-	9.852%
2022-08-17	axn	Manual testing	50000000	1263691439010		-		-	-	2,423	-	-	21.886%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-11-11	masser	Manual testing	2000000	72000000	191	67			-	-	0.238
2022-11-11	masser	Manual testing	8000000	400000000	2	7			-	-	1.164
2022-11-11	masser	Manual testing	4000000	172000000	6	5	40875951889311160318482553348879	P+1	32	105.011	0.529

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-06-28	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.005	-	-
2000-06-29	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.005	-	-
2000-12-07	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.010	-	-
2001-10-20	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.021	-	-
2003-08-25	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.041	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.124	-	-
2010-05-22	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.165	-	-
2014-08-14	lycorn	Manual testing	2⁶¹	2⁶²		-	-	0.329	-	-
2015-09-19	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.053	-	-
2015-09-19	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.105	-	-
2015-12-30	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	4.007	-	-
2018-01-05	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	8.013	-	-
2018-01-05	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	16.03	-	-
2018-01-05	Smok_bmv	Manual testing	2⁶⁷	2⁶⁸		-	-	32.05	-	-

ECM factoring results:

Total ECM effort:	25.916 GHz-days
Estimated T-Level:	25.941

Digits	B1	Complete	FacMiss
20	11000	15.520	0.000%
25	50000	1.986	13.720%
30	250000	0.188	82.838%
35	1000000	0.014	98.565%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	200	5.641
250000	25000000	41	5.782
250000	50000000	16	3.074
250000	235419030	20	11.42

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-10	Chad Davis	Bayes	50000	5000000						1	0.028
2008-02-05	arnaud	CHAMOT27	50000	5000000						3	0.085
2008-11-05	Sturle Sunde	v21	50000	5000000						3	0.085
2009-02-24	Sturle Sunde	v21	50000	5000000						3	0.085
2009-07-07	Lackó	Iroda_Eva	50000	5000000						3	0.085
2009-09-16	ClknGo Software Corp	cngs1	50000	5000000						3	0.085
2009-11-28	maxybo	CB418E216	50000	5000000						3	0.085
2010-04-06	toji	tablepc2	50000	5000000						3	0.085
2010-11-09	maxybo	CB418E216	50000	5000000						3	0.085
2011-02-14	Boots	technomicron	50000	5000000						3	0.085
2011-11-10	unconnected	can-01	50000	5000000						3	0.085
2012-05-12	Pool Party	sts	50000	5000000						3	0.085
2012-09-08	alpertron	core2quad	50000	5000000						3	0.085
2013-02-06	gucs	echo3	50000	5000000						3	0.085
2013-04-26	gucs	echo3	50000	5000000						3	0.085
2013-07-18	gucs	echo3	50000	5000000						3	0.085
2013-10-10	alpertron	core2quad	50000	5000000						3	0.085
2013-12-28	gucs	echo3	50000	5000000						3	0.085
2014-02-23	Ryan Schulz	wenn	50000	5000000						15	0.423
2015-02-26	Bruce	desk16	50000	5000000						3	0.085
2015-05-12	Sergiosi	Manual testing	50000	5000000						130	3.666
2015-09-12	westicles	Manual testing	250000	50000000						16	3.074
2019-10-21	TJAOI	Manual testing	250000	25000000						41	5.782
2022-09-20	axn	Manual testing	250000	235419030						20	11.42

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Mr. McGrath		30A086AD77F7E071	0.023
2001-12-01	ANONYMOUS	v4_computers	30A086AD77F7E071	0.023
2015-04-11	MadPoo	Manual testing	30A086AD77F7E071	0.023

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-11-11

Kevin_9611

PRP-CF

40875951889311160318482553348879

30863A44BD0DC1FE

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 = 50000000, B2 = 1263691439010 (P-1 stage 2)

B1 = 50000000 (P-1 stage 1)

B1 = 10000000, B2 = 500000000 (P-1 stage 2)

B1 = 4000000, B2 = 172000000 (P+1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 4000000 (P+1 stage 1)

B1 = 870000, B2 = 26100000 (P-1 stage 2)

B1 = 870000 (P-1 stage 1)

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

B1 = 727399 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 363699 (P-1 stage 1)

B1 = 218219 (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 = 65536 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=25.94 ~= 70-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2023-04-26T21:34:10+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