M803 449 Mersenne number exponent details

is 2 ⁸⁰³⁴⁴⁹ - 1

has 241863 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	2⁷⁰	297.4061	71.4286%	8027770	501024934410	790.7397	16.2452%	1,088.1458	76.0700%
Target	2⁴⁴	0.0000	54.5455%	13000	4000000	0.0067	17.1268%	0.0067	62.3303%
Difference	+26	+297.4061	+16.8831%	+8014770	+501020934410	+790.7331	-0.8816%	+1,088.1392	+13.7397%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
803449	125923529978589219526674704914180518967	39	126.566	78364357898627803088108084591667 3 × 43 × 8702596057 × 69803957192336191339	2023-09-10	8702596057	69803957192336191339	2.381e+11	1.101e+11	2.057e+11

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	-	-	0.105%
2002-02-10	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.243%
2002-03-31	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.469%
2002-05-11	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	0.805%
2002-06-02	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.263%
2002-11-16	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	1.849%
2003-07-06	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	2.558%
2012-08-01	Jocelyn Larouche	Manual testing	1606898	1606898		-		-	-	0.047	-	-	2.037%
2013-10-25	David Campeau	i5-2500k	1650000	56100000		-		-	-	0.134	-	-	5.069%
2015-11-24	Sid & Andy	Woody	8034490	241034700	12	-		-	-	0.600	-	-	7.411%
2022-04-04	lycorn	colab_A	8027770	501024934410		-		-	-	790.7	-	-	16.245%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-09-13	gLauss	Manual testing	7500000	585000000	2	7			-	-	1.223
2023-09-10	masser	Manual testing	10000000	10000000	174	23	125923529978589219526674704914180518967	P+1	39	126.566	0.440

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-17	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2000-12-21	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-10-06	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.024	-	-
2003-08-25	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.048	-	-
2008-10-12	Sturle Sunde	scarpia.ifi	2⁵⁸	2⁵⁹		-	-	0.048	-	-
2008-10-12	Sturle Sunde	scarpia.ifi	2⁵⁹	2⁶⁰		-	-	0.096	-	-
2010-05-25	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.191	-	-
2015-01-16	snme2pm1	G1	2⁶¹	2⁶²		-	-	0.382	-	-
2015-09-26	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.222	-	-
2015-09-26	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.444	-	-
2016-03-01	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	4.650	-	-
2017-06-16	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	9.301	-	-
2017-06-19	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	18.60	-	-
2017-06-19	Smok_bmv	Manual testing	2⁶⁷	2⁶⁸		-	-	37.20	-	-
2019-11-09	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	74.41	-	-
2019-11-09	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	148.8	-	-

ECM factoring results:

Total ECM effort:	1,650.420 GHz-days
Estimated T-Level:	28.145

Digits	B1	Complete	FacMiss
20	11000	41.010	0.000%
25	50000	6.005	0.247%
30	250000	0.629	53.313%
35	1000000	0.052	94.921%
40	3000000	0.004	99.647%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	343	7.839
250000	25000000	31	3.542
350000	4962111924	200	1,639

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-02	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-19	Steve Scott	Abit-2	50000	5000000						3	0.069
2008-09-27	Sturle Sunde	v23	50000	5000000						3	0.069
2009-01-10	Sturle Sunde	v21	50000	5000000						3	0.069
2009-03-25	Sturle Sunde	v23	50000	5000000						3	0.069
2009-07-16	SubPrime	c2d0	50000	5000000						3	0.069
2009-09-20	JimBa	atlserv	50000	5000000						3	0.069
2009-11-24	greensinoz	giopa01	50000	5000000						3	0.069
2010-03-12	toji	tablepc2	50000	5000000						3	0.069
2010-08-23	unconnected	xp-lm	50000	5000000						3	0.069
2011-01-11	arnaud	Arnaud-PC	50000	5000000						3	0.069
2011-01-29	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-10-12	Andriy Makukha	freehost	50000	5000000						3	0.069
2012-01-16	Pool Party	sts	50000	5000000						3	0.069
2012-07-22	soldake		50000	5000000						3	0.069
2012-10-23	RHMash	laptop	50000	5000000						3	0.069
2013-02-11	gucs	echo3	50000	5000000						3	0.069
2013-04-21	gucs	echo3	50000	5000000						3	0.069
2013-06-27	gucs	echo3	50000	5000000						3	0.069
2013-09-04	gucs	echo3	50000	5000000						3	0.069
2013-11-14	gucs	echo3	50000	5000000						3	0.069
2014-01-24	gucs	echo3	50000	5000000						3	0.069
2014-03-05	gucs	echo3	50000	5000000						3	0.069
2014-04-04	gucs	echo3	50000	5000000						3	0.069
2014-05-03	gucs	echo3	50000	5000000						3	0.069
2014-11-15	Ryan Schulz	wenn	50000	5000000						15	0.343
2015-12-04	TJAOI	Manual testing	50000	5000000						14	0.320
2016-02-04	Bruce	Desk6	50000	5000000						3	0.069
2016-02-06	Bruce	Desk6	50000	5000000						3	0.069
2016-02-07	Bruce	Desk6	50000	5000000						3	0.069
2016-02-09	Bruce	Desk6	50000	5000000						3	0.069
2016-02-11	Bruce	Desk6	50000	5000000						3	0.069
2016-02-13	Bruce	Desk6	50000	5000000						3	0.069
2016-02-15	Bruce	Desk6	50000	5000000						3	0.069
2016-02-17	Bruce	Desk6	50000	5000000						3	0.069
2016-02-19	Bruce	Desk6	50000	5000000						3	0.069
2016-05-29	Oussama Kiamouche	Home	50000	5000000						3	0.069
2016-06-30	westicles	Manual testing	50000	5000000						150	3.428
2016-10-07	TJAOI	Manual testing	50000	5000000						63	1.440
2019-12-16	TJAOI	Manual testing	250000	25000000						31	3.542
2023-06-01	lycorn	supernova	350000	4962111924						200	1,639

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Dieter Stahel		BA20BD5FE34B289D	0.016
2015-04-11	MadPoo	Manual testing	BA20BD5FE34B289D	0.016

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-09-10

masser

Manual testing

125923529978589219526674704914180518967

38ADC799D672BB86

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 = 8027770, B2 = 501024934410 (P-1 stage 2)

B1 = 8034490, B2 = 241034700 (P-1 stage 2)

B1 = 10000000 (P+1 stage 1)

B1 = 8034490 (P-1 stage 1)

B1 = 8027770 (P-1 stage 1)

B1 = 1650000, B2 = 56100000 (P-1 stage 2)

B1 = 1650000 (P-1 stage 1)

B1 = 1606898 (P-1 stage 1)

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

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

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

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10⁶

10⁷

10⁸

10⁹

10¹⁰

10²

10³

10⁴

10⁵

10⁶

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10⁸

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10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=28.14 ~= 77-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2023-09-10T01:47:46+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