M101 141 Mersenne number exponent details

is 2 ¹⁰¹¹⁴¹ - 1

has 30447 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	293.7871	74.6269%	1000000000	6544247689980	1,151.9257	25.4548%	1,445.7128	81.0856%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1578%	0.0000	62.9701%
Difference	+23	+293.7870	+13.2632%	+999998800	+6544247671980	+1,151.9257	+21.2970%	+1,445.7127	+18.1155%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101141	3353019149849	13	41.609	16575964 2² × 73 × 56767	-	73	56767	5.419e-6	1.019e-5	1.861e-5
101141	1454578143980119	16	50.370	7190843199 3 × 89 × 26931997	2009-01-25	89	26931997	0.0023	0.0047	0.0088

exponent	prime factors	composite factor	digits	bits*
101141	3353019149849 1454578143980119	4877228371717154926537852031	28	91.978

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: 3353019149849 skipped known factor: 1454578143980119	-	-	0.656	-	-	11.733%
2021-12-17	Seth_Tr	Manual testing	1000000000	6544247689980		-	skipped known factor: 3353019149849 skipped known factor: 1454578143980119	-	-	1,152	-	-	25.455%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-25	George Woltman	Manual testing	?	?	1454578143980119	50.370	16	0.001	0.000	0.002
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	1454578143980119	50.370	16	0.002	0.000	0.005
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	3353019149849	41.609	13	5.41925e-6	0.000	1.14219e-5
2018-11-02	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.759	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.759	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.519	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.037	-	-
2022-12-08	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.71	-	-
2022-12-08	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.41	-	-
2022-12-08	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	36.94	-	-

ECM factoring results:

Total ECM effort:	12.597 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
2017-02-18	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-28	storm5510	HP-Z220-CMT	1000000	100000000						3	0.139
2019-04-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-12	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-01	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M101141

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Doppelherz

3353019149849

1454578143980119

8276CCAFB15D65__

2017-09-21

Oliver Kruse

Manual testing

3353019149849

1454578143980119

8276CCAFB15D65__

2017-09-22

Oliver Kruse

Manual testing

3353019149849

1454578143980119

8276CCAFB15D65__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

3353019149849

1454578143980119

8276CCAFB15D65__

2020-04-17

Oliver Kruse

AddPrpType5

3353019149849

1454578143980119

B8991D408E33FB__

2022-04-15

LordJulius

WhiteBox

3353019149849

1454578143980119

B8991D408E33FB35

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 = 6544247689980 (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

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10⁴

10⁵

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10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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10¹³

TF factor-bounds graph:

2⁶⁵

2⁶⁴

2⁶³

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: 2023-04-26T21:34:10+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