M782 669 Mersenne number exponent details

is 2 ⁷⁸²⁶⁶⁹ - 1

has 235607 decimal digits

takes 0.016 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
Actual	2⁶⁸	76.1559	70.5882%	10000000	127825247550	201.9572	16.8410%	278.1131	75.5415%
Target	2⁴⁴	0.0000	54.5455%	13000	4000000	0.0067	17.0767%	0.0067	62.3076%
Difference	+24	+76.1559	+16.0428%	+9987000	+127821247550	+201.9505	-0.2357%	+278.1065	+13.2339%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
782669	880362581741385337324999	24	79.542	562410534811897071 3² × 204517 × 305549462507	2023-04-28	204517	305549462507	174,410	482.10	900.42

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-02	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.162%
2002-02-03	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.357%
2002-03-31	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.659%
2002-05-18	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.090%
2002-07-27	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.660%
2002-12-09	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.368%
2003-07-21	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.202%
2011-07-10	Jocelyn Larouche	Manual testing	273884	273884		-		-	-	0.008	-	-	1.166%
2011-08-28	Jocelyn Larouche	Manual testing	456474	456474		-		-	-	0.013	-	-	1.494%
2012-01-09	Jocelyn Larouche	Manual testing	912949	912949		-		-	-	0.026	-	-	2.019%
2012-07-14	Jocelyn Larouche	Manual testing	1565338	1565338		-		-	-	0.045	-	-	2.490%
2013-10-29	David Campeau	i5-2500k	1625000	55250000		-		-	-	0.132	-	-	6.011%
2015-11-20	Sid & Andy	Speck	7826690	234800700	12	-		-	-	0.585	-	-	8.580%
2022-02-11	LordJulius	WhiteBox_v308	10000000	127825247550		-		-	-	202.0	-	-	16.841%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2023-04-01	masser	Manual testing	6000000	288000000	2	7			-	-	0.700
2023-04-03	masser	Manual testing	6000000	276000000	171	53			-	-	0.682
2023-04-28	masser	Manual testing	6000000	276000000	6	5	880362581741385337324999	P+1	24	79.542	0.682

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-10-07	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-18	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-12-08	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.025	-	-
2003-09-21	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.049	-	-
2008-10-13	Sturle Sunde	rodolfo.ifi	2⁵⁸	2⁵⁹		-	-	0.049	-	-
2008-10-13	Sturle Sunde	rodolfo.ifi	2⁵⁹	2⁶⁰		-	-	0.098	-	-
2010-06-24	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.196	-	-
2015-03-07	NR	Manual testing	2⁶¹	2⁶²		-	-	0.392	-	-
2015-10-22	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.254	-	-
2015-10-22	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.508	-	-
2016-03-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	4.774	-	-
2017-11-22	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	9.55	-	-
2020-02-22	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	19.10	-	-
2022-03-06	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	38.19	-	-

ECM factoring results:

Total ECM effort:	11.397 GHz-days
Estimated T-Level:	25.656

Digits	B1	Complete	FacMiss
20	11000	14.769	0.000%
25	50000	1.616	19.866%
30	250000	0.131	87.697%
35	1000000	0.009	99.130%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	6.382
250000	25000000		44	5.014

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-01	Team_Bundu	bundu1	50000	5000000						1	0.023
2008-01-18	Steve Scott	Asus-2	50000	5000000						3	0.068
2008-09-22	Sturle Sunde	v23	50000	5000000						3	0.068
2008-12-29	Sturle Sunde	v24	50000	5000000						3	0.068
2009-03-18	Sturle Sunde	v21	50000	5000000						3	0.068
2009-07-07	arnaud	SRV-150	50000	5000000						3	0.068
2009-09-10	SubPrime	c2d0	50000	5000000						3	0.068
2009-11-04	GrunwalderGIMP	compute-0-9	50000	5000000						3	0.068
2010-02-17	sannerud.com	snap1	50000	5000000						3	0.068
2010-06-19	josibo	Ziben	50000	5000000						3	0.068
2010-12-25	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.068
2011-02-01	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-06-25	maxybo	CB418E216	50000	5000000						3	0.068
2011-11-30	Hackster Lim	limlianhing	50000	5000000						3	0.068
2012-05-27	Pool Party	sts	50000	5000000						3	0.068
2012-08-25	soldake		50000	5000000						3	0.068
2013-01-09	gucs	echo3	50000	5000000						3	0.068
2013-03-22	gucs	echo3	50000	5000000						3	0.068
2013-05-30	gucs	echo3	50000	5000000						3	0.068
2013-08-07	gucs	echo3	50000	5000000						3	0.068
2013-10-08	gucs	echo3	50000	5000000						3	0.068
2013-12-19	gucs	echo3	50000	5000000						3	0.068
2014-02-07	Ryan Schulz	wenn	50000	5000000						15	0.342
2015-02-21	Bruce	desk16	50000	5000000						3	0.068
2015-02-24	Bruce	desk16	50000	5000000						3	0.068
2015-03-01	Bruce	desk16	50000	5000000						3	0.068
2015-11-20	TJAOI	Manual testing	50000	5000000						14	0.319
2016-02-07	yooper		50000	5000000						150	3.419
2016-04-30	westicles	Manual testing	50000	5000000						30	0.684
2017-08-09	codest	web	250000	25000000						3	0.342
2017-10-18	jafarism	jafarism-r06-26	250000	25000000						3	0.342
2019-03-01	TJAOI	Manual testing	250000	25000000						38	4.331

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Larry English		28119EC7D35E857D	0.016
2015-04-11	MadPoo	Manual testing	28119EC7D35E857D	0.016

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-04-28

masser

Manual testing

880362581741385337324999

0DA8A84A7E9A5F41

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 = 10000000, B2 = 127825247550 (P-1 stage 2)

B1 = 6000000, B2 = 276000000 (P+1 stage 2)

B1 = 7826690, B2 = 234800700 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 7826690 (P-1 stage 1)

B1 = 6000000 (P+1 stage 1)

B1 = 1625000, B2 = 55250000 (P-1 stage 2)

B1 = 1625000 (P-1 stage 1)

B1 = 1565338 (P-1 stage 1)

B1 = 912949 (P-1 stage 1)

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

B1 = 456474 (P-1 stage 1)

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

B1 = 273884 (P-1 stage 1)

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

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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=25.66 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-06-05T21:50:05+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