M778 213 Mersenne number exponent details

is 2 ⁷⁷⁸²¹³ - 1

has 234266 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	76.5920	70.5882%	1000000	13912959060	21.9793	11.2659%	98.5713	73.9017%
Target	2⁴⁴	0.0000	54.5455%	13000	4000000	0.0067	17.0658%	0.0067	62.3027%
Difference	+24	+76.5920	+16.0428%	+987000	+13908959060	+21.9727	-5.7999%	+98.5646	+11.5991%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
778213	108366466090775000476999409	27	86.486	69625196501969898008 2³ × 8703149562746237251	2023-03-20	8	8703149562746237251	33,510,637	1.373e+10	2.565e+10

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.009	-	-	2.371%
2002-06-02	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.089%
2002-07-27	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.659%
2002-12-09	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.366%
2003-07-21	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.200%
2011-07-10	Jocelyn Larouche	Manual testing	275919	275919		-		-	-	0.008	-	-	1.169%
2011-08-28	Jocelyn Larouche	Manual testing	459866	459866		-		-	-	0.013	-	-	1.498%
2011-12-17	Jocelyn Larouche	Manual testing	919732	919732		-		-	-	0.027	-	-	2.023%
2012-07-14	Jocelyn Larouche	Manual testing	1556426	1556426		-		-	-	0.045	-	-	2.483%
2013-10-28	David Campeau	i5-2500k	1620000	55080000		-		-	-	0.131	-	-	6.002%
2015-11-22	Sid & Andy	Speck	7782130	233463900	12	-		-	-	0.581	-	-	8.565%
2022-11-24	Jocelyn Larouche	Manual testing	1621000	4929814890		-		-	-	7.823	-	-	10.784%
2023-03-22	Jocelyn Larouche	Manual testing	1000000	13912959060		-		-	-	21.98	-	-	11.266%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2023-03-20	masser	Manual testing	6000000	6000000	2	7	108366466090775000476999409	P+1	27	86.486	0.264
2023-03-20	masser	Manual testing	6000000	6000000	135	17	108366466090775000476999409	P+1	27	86.486	0.264
2023-04-28	masser	Manual testing	6000000	276000000	6	5			-	-	0.682

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-09-29	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-25	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-12-22	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.025	-	-
2003-09-21	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.049	-	-
2008-10-17	Sturle Sunde	jaipur.ifi	2⁵⁸	2⁵⁹		-	-	0.049	-	-
2008-10-17	Sturle Sunde	jaipur.ifi	2⁵⁹	2⁶⁰		-	-	0.099	-	-
2010-06-14	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.197	-	-
2015-03-06	NR	Manual testing	2⁶¹	2⁶²		-	-	0.395	-	-
2015-10-25	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.261	-	-
2015-10-25	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.523	-	-
2016-03-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	4.801	-	-
2018-03-23	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	9.60	-	-
2020-03-08	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	19.20	-	-
2022-03-14	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	38.41	-	-

ECM factoring results:

Total ECM effort:	12.321 GHz-days
Estimated T-Level:	25.719

Digits	B1	Complete	FacMiss
20	11000	15.506	0.000%
25	50000	1.730	17.726%
30	250000	0.144	86.600%
35	1000000	0.010	99.025%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	280	6.378
250000	25000000	51	5.809
250000	37250000	1	0.134

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-01	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-18	Sturle Sunde	minister	50000	5000000						3	0.068
2008-09-21	Sturle Sunde	v21	50000	5000000						3	0.068
2008-12-23	Sturle Sunde	v23	50000	5000000						3	0.068
2009-03-17	Sturle Sunde	v21	50000	5000000						3	0.068
2009-07-04	maxybo	CB418E216	50000	5000000						3	0.068
2009-09-08	JimBa	HPserv	50000	5000000						3	0.068
2009-11-02	JimBa	atlserv	50000	5000000						3	0.068
2010-02-10	Lupo	yorick	50000	5000000						3	0.068
2010-06-16	Charles A. Morris	pulsar	50000	5000000						3	0.068
2010-12-19	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.068
2011-01-30	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-04-18	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.068
2011-11-22	OS1	Tina	50000	5000000						3	0.068
2012-05-06	Pool Party	sts	50000	5000000						3	0.068
2012-05-06	Pool Party	sts	50000	5000000						3	0.068
2013-01-02	gucs	echo3	50000	5000000						3	0.068
2013-03-16	gucs	echo3	50000	5000000						3	0.068
2013-05-23	gucs	echo3	50000	5000000						3	0.068
2013-07-28	gucs	echo3	50000	5000000						3	0.068
2013-09-30	gucs	echo3	50000	5000000						3	0.068
2013-12-11	gucs	echo3	50000	5000000						3	0.068
2014-02-12	Bruce	snowflake	50000	5000000						3	0.068
2014-03-16	gucs	echo3	50000	5000000						3	0.068
2014-04-11	gucs	echo3	50000	5000000						3	0.068
2014-05-07	gucs	echo3	50000	5000000						3	0.068
2014-11-15	Ryan Schulz	wenn	50000	5000000						15	0.342
2016-01-12	maxa	maxa-srv	50000	5000000						3	0.068
2016-01-26	Oussama Kiamouche	Home	50000	5000000						3	0.068
2016-02-19	Fastspiky	Manual testing	50000	5000000						150	3.417
2016-05-03	westicles	Manual testing	50000	5000000						35	0.797
2019-03-01	TJAOI	Manual testing	250000	25000000						44	5.012
2022-12-27	arnaud	ATTAX04	250000	25000000						7	0.797
2023-03-02	carlos56	velero	250000	37250000						1	0.134

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Peter Marksteiner		23872C0B4EBC5F23	0.016
2002-10-26	ANONYMOUS	v4_computers	23872C0B4EBC5F23	0.016
2015-04-11	MadPoo	Manual testing	23872C0B4EBC5F23	0.016

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-03-20

masser

Manual testing

108366466090775000476999409

072F5C9F5BBFAFA9

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 = 13912959060 (P-1 stage 2)

B1 = 1621000, B2 = 4929814890 (P-1 stage 2)

B1 = 7782130, B2 = 233463900 (P-1 stage 2)

B1 = 7782130 (P-1 stage 1)

B1 = 6000000 (P+1 stage 1)

B1 = 1620000, B2 = 55080000 (P-1 stage 2)

B1 = 1621000 (P-1 stage 1)

B1 = 1620000 (P-1 stage 1)

B1 = 1556426 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 919732 (P-1 stage 1)

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

B1 = 459866 (P-1 stage 1)

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

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 275919 (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 = 100000 (P-1 stage 1)

B1 = 65537 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10⁰

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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=25.72 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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