M101 411 Mersenne number exponent details

is 2 ¹⁰¹⁴¹¹ - 1

has 30528 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	293.0049	74.6269%	1000000000	6736600110240	1,185.6942	25.5010%	1,478.6991	81.0973%
Target	2⁴⁴	0.0000	61.3636%	1300	18000	0.0000	4.2574%	0.0000	63.0085%
Difference	+23	+293.0049	+13.2632%	+999998700	+6736600092240	+1,185.6942	+21.2436%	+1,478.6991	+18.0887%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101411	202823	6	17.630	1 1	-	1	1	1.722e-13	3.222e-9	6.558e-9
101411	18862447	8	24.169	93 3 × 31	2008-07-26	3	31	2.248e-11	1.458e-8	1.967e-8
101411	520611622481	12	38.921	2566840 2³ × 5 × 64171	2008-07-26	8	64171	5.752e-7	1.129e-5	2.104e-5

exponent	prime factors	composite factor	digits	bits*
101411	202823 18862447	3825738087881	13	41.799
101411	202823 520611622481	105592011106463863	18	56.551
101411	18862447 520611622481	9820009136631871007	19	63.090
101411	202823 18862447 520611622481	1991723713119085973252761	25	80.720

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: 202823 skipped known factor: 18862447 skipped known factor: 520611622481	-	-	0.656	-	-	11.736%
2021-12-18	Seth_Tr	Manual testing	1000000000	6736600110240		-	skipped known factor: 202823 skipped known factor: 18862447 skipped known factor: 520611622481	-	-	1,186	-	-	25.501%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-26	J Feitsma	Manual testing	?	?	18862447	24.169	8	4.43649e-13	0.000	9.46811e-13
2008-07-26	J Feitsma	Manual testing	?	?	520611622481	38.921	12	2.14154e-7	0.000	4.56350e-7
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	202823 520611622481	56.551	18	0.186	0.000	0.378
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	18862447	24.169	8	2.24830e-11	0.000	4.79819e-11
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	202823	17.630	6	1.72217e-13	0.000	3.67536e-13
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	202823 18862447	41.799	13	5.20223e-6	0.000	1.09689e-5
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	520611622481	38.921	12	5.75247e-7	0.000	1.22582e-6
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		-	-	0.757	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.515	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.029	-	-

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
2017-03-06	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-27	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-22	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-29	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-X	1000000	100000000						3	0.139
2019-05-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-21	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
2019-06-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-12	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
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-10	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M101411

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

202823

18862447

520611622481

4D74080C20F98C__

2017-09-21

Oliver Kruse

Manual testing

202823

18862447

520611622481

4D74080C20F98C__

2017-10-13

kkmrkkblmbrbk

Manual testing

202823

18862447

520611622481

4D74080C20F98C__

2020-04-17

Oliver Kruse

AddPrpType5

202823

18862447

520611622481

FBBB32C369853F__

2022-04-15

LordJulius

WhiteBox

202823

18862447

520611622481

FBBB32C369853FEE

2022-05-12

Jorge Coveiro

Manual testing

202823

FBBB32C369853FEE

2022-11-05

LordJulius

WhiteBox

202823

18862447

520611622481

FBBB32C369853FEE

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 = 6736600110240 (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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10³

10⁴

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10¹³

TF factor-bounds graph:

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=30.76 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-03-25T13:08:14+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