M101 347 Mersenne number exponent details

is 2 ¹⁰¹³⁴⁷ - 1

has 30509 decimal digits

takes 0.000 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	2⁶⁷	293.1899	74.6269%	1000000000	6735532633830	1,185.5068	25.5001%	1,478.6967	81.0970%
Target	2⁴⁴	0.0000	61.3636%	1200	144000	0.0000	4.1597%	0.0001	62.9708%
Difference	+23	+293.1899	+13.2632%	+999998800	+6735532489830	+1,185.5068	+21.3404%	+1,478.6967	+18.1262%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101347	9358067492151241	16	53.055	46168448460 2² × 3 × 5 × 19 × 79 × 512641	2014-04-23	79	512641	0.0197	9.024e-5	0.0002

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-11-02	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 9358067492151241	-	-	0.656	-	-	11.735%
2021-12-18	Seth_Tr	Manual testing	1000000000	6735532633830		-	skipped known factor: 9358067492151241	-	-	1,186	-	-	25.500%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	9358067492151241	53.055	16	0.020	0.000	0.040
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.189	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.515	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.031	-	-

ECM factoring results:

Total ECM effort:	12.598 GHz-days
Estimated T-Level:	30.756

Digits	B1	Complete	FacMiss
20	11000	82.490	0.000%
25	50000	12.939	0.000%
30	250000	1.545	21.330%
35	1000000	0.151	85.963%
40	3000000	0.013	98.746%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	0.652
250000	25000000	585	6.791
1000000	100000000	111	5.154

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-04-20	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-04-11	TJAOI	Manual testing	50000	5000000						38	0.088
2014-05-13	TJAOI	Manual testing	50000	5000000						231	0.536
2017-03-03	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-28	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-19	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-02-07	ANONYMOUS	v4_computers	CB255CAC7D250D__	0.000

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

9358067492151241

73E81857A1AD7E__

2017-09-21

Oliver Kruse

Manual testing

9358067492151241

73E81857A1AD7E__

2017-10-13

kkmrkkblmbrbk

Manual testing

9358067492151241

73E81857A1AD7E__

2020-04-17

Oliver Kruse

AddPrpType5

9358067492151241

E7C9A43AA4EC60__

2022-04-15

LordJulius

WhiteBox

9358067492151241

E7C9A43AA4EC604E

2022-10-27

LordJulius

WhiteBox

9358067492151241

E7C9A43AA4EC604E

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 = 1000000000, B2 = 6735532633830 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=30.76 ~= 86-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