M746 107 Mersenne number exponent details

is 2 ⁷⁴⁶¹⁰⁷ - 1

has 224601 decimal digits

takes 0.015 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	79.8878	70.5882%	7600000	1203456454200	1,899.0284	19.1557%	1,978.9162	76.2223%
Target	2⁴⁴	0.0000	54.5455%	12000	3600000	0.0060	16.6205%	0.0060	62.1002%
Difference	+24	+79.8878	+16.0428%	+7588000	+1203452854200	+1,899.0224	+2.5352%	+1,978.9102	+14.1221%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
746107	142033587586045547693689743564409	33	106.808	95183122250592440289187572 2² × 3 × 9587 × 293263 × 2821231344318251	2023-04-08	293263	2821231344318251	2.494e+11	4,451,354	8,313,891

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	-	-	2.356%
2002-05-25	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.080%
2002-11-24	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.350%
2003-06-30	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.180%
2011-06-21	Jocelyn Larouche	Manual testing	400000	400000		-		-	-	0.012	-	-	1.394%
2011-08-15	Jocelyn Larouche	Manual testing	485686	485686		-		-	-	0.014	-	-	1.526%
2011-10-22	Jocelyn Larouche	Manual testing	971373	971373		-		-	-	0.028	-	-	2.056%
2012-07-14	Jocelyn Larouche	Manual testing	1492214	1492214		-		-	-	0.043	-	-	2.430%
2013-10-27	David Campeau	i5-2500k	1520000	51680000		-		-	-	0.123	-	-	5.873%
2015-11-22	Sid & Andy	Speck	7461070	223832100	12	-		-	-	0.557	-	-	8.456%
2022-05-05	lycorn	supernova	7600000	1203456454200		-		-	-	1,899	-	-	19.156%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2023-04-08	masser	Manual testing	7000000	336000000	2	7			-	-	0.719
2023-04-08	masser	Manual testing	7000000	322000000	151	23	142033587586045547693689743564409	P+1	33	106.808	0.700
2023-04-28	masser	Manual testing	7000000	336000000	6	5			-	-	0.719

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-09-08	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-03-25	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.013	-	-
2001-12-08	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.026	-	-
2003-09-29	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.051	-	-
2008-10-11	Sturle Sunde	nouchcraft.ifi	2⁵⁸	2⁵⁹		-	-	0.051	-	-
2008-10-12	Sturle Sunde	nouchcraft.ifi	2⁵⁹	2⁶⁰		-	-	0.103	-	-
2010-05-31	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.206	-	-
2015-03-05	NR	Manual testing	2⁶¹	2⁶²		-	-	0.412	-	-
2015-10-20	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.316	-	-
2015-10-20	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.631	-	-
2016-04-08	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	5.008	-	-
2017-10-09	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	10.02	-	-
2020-05-15	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	20.03	-	-
2022-03-22	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	40.06	-	-

ECM factoring results:

Total ECM effort:	15.734 GHz-days
Estimated T-Level:	25.943

Digits	B1	Complete	FacMiss
20	11000	18.078	0.000%
25	50000	2.132	11.858%
30	250000	0.189	82.804%
35	1000000	0.014	98.648%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	280	6.353
250000	25000000	58	6.579
250000	27500000	7	0.822
250000	37250000	7	0.932
250000	47599650	7	1.048

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-30	Team_Bundu	bundu1	50000	5000000						1	0.023
2008-01-04	Steve Scott	Asus-1	50000	5000000						1	0.023
2008-01-04	Steve Scott	Asus-1	50000	5000000						1	0.023
2008-08-04	Scott Kurowski	UW1	50000	5000000						3	0.068
2008-11-18	Sturle Sunde	v21	50000	5000000						3	0.068
2010-05-12	Bud	annan	50000	5000000						3	0.068
2010-05-13	maxybo	CB418E216	50000	5000000						3	0.068
2010-05-13	sannerud.com	strs-w2k8e	50000	5000000						3	0.068
2010-05-14	sannerud.com	snap1	50000	5000000						3	0.068
2010-05-14	toji	tablepc2	50000	5000000						3	0.068
2010-05-15	maxybo	CB418E216	50000	5000000						3	0.068
2010-05-16	Bud	annan	50000	5000000						3	0.068
2011-01-04	maxybo	CB418E216	50000	5000000						3	0.068
2011-03-12	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-08-07	Boots	technomicron	50000	5000000						3	0.068
2011-11-30	Andriy Makukha	freehost	50000	5000000						3	0.068
2012-05-19	Pool Party	sts	50000	5000000						3	0.068
2012-08-20	soldake		50000	5000000						3	0.068
2012-12-30	gucs	echo3	50000	5000000						3	0.068
2013-03-10	gucs	echo3	50000	5000000						3	0.068
2013-05-09	gucs	echo3	50000	5000000						3	0.068
2013-07-13	gucs	echo3	50000	5000000						3	0.068
2013-09-17	gucs	echo3	50000	5000000						3	0.068
2013-11-20	gucs	echo3	50000	5000000						3	0.068
2014-01-24	Ryan Schulz	wenn-old	50000	5000000						15	0.340
2014-12-19	Ryan Schulz	wenn	50000	5000000						15	0.340
2015-10-30	TJAOI	Manual testing	50000	5000000						6	0.136
2016-02-08	Fastspiky	Manual testing	50000	5000000						150	3.403
2016-04-30	westicles	Manual testing	50000	5000000						30	0.681
2018-01-03	jafarism	jafarism-r01	250000	25000000						3	0.340
2019-01-25	TJAOI	Manual testing	250000	25000000						41	4.651
2022-02-27	Oliver Kruse	Krusen-NAS	250000	37250000						7	0.932
2022-06-09	prime23	work	250000	27500000						7	0.822
2022-11-13	arnaud	ATTAX04	250000	25000000						7	0.794
2022-11-13	arnaud	ATTAX04	250000	25000000						7	0.794
2022-12-28	storm5510	3570IB	250000	47599650						7	1.048

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Ken Kriesel		E666F24709656817	0.015
2002-10-19	ANONYMOUS	v4_computers	E666F24709656817	0.015
2015-04-11	MadPoo	Manual testing	E666F24709656817	0.015

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-04-08

masser

Manual testing

142033587586045547693689743564409

4339960BD1330F__

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 = 7600000, B2 = 1203456454200 (P-1 stage 2)

B1 = 7000000, B2 = 322000000 (P+1 stage 2)

B1 = 7461070, B2 = 223832100 (P-1 stage 2)

B1 = 7600000 (P-1 stage 1)

B1 = 7461070 (P-1 stage 1)

B1 = 7000000 (P+1 stage 1)

B1 = 1520000, B2 = 51680000 (P-1 stage 2)

B1 = 1520000 (P-1 stage 1)

B1 = 1492214 (P-1 stage 1)

B1 = 971373 (P-1 stage 1)

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

B1 = 485686 (P-1 stage 1)

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

B1 = 400000 (P-1 stage 1)

B1 = 100000, B2 = 4000000 (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 = 16384 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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=25.94 ~= 70-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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