M101 341 Mersenne number exponent details

is 2 ¹⁰¹³⁴¹ - 1

has 30507 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	293.2073	74.6269%	1000000000	6735532633830	1,185.5068	25.5000%	1,478.7141	81.0970%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1596%	0.0000	62.9708%
Difference	+23	+293.2072	+13.2632%	+999998800	+6735532615830	+1,185.5068	+21.3403%	+1,478.7141	+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
101341	1537187248608673	16	50.449	7584231696 2⁴ × 3 × 67 × 401 × 5881	2014-04-23	401	5881	0.0024	2.254e-6	2.630e-6
101341	21633883830589081985481137	26	84.161	106738061744945688248 2³ × 1949 × 78350599 × 87372581	2016-10-30	78350599	87372581	53,789,619	0.2540	0.5138

exponent	prime factors	composite factor	digits	bits*
101341	1537187248608673 21633883830589081985481137	33255330362262890128924273240289736101201	41	134.611

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-10-30	kkmrkkblmbrbk	Manual testing	100000000	100000000			21633883830589081985481137	26	84.161	0.322	0.000	0.644	7.023%
2021-12-19	Seth_Tr	Manual testing	1000000000	6735532633830		-	skipped known factor: 1537187248608673 skipped known factor: 21633883830589081985481137	-	-	1,186	-	-	25.500%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	1537187248608673	50.449	16	0.002	0.000	0.005
2018-11-02	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.189	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.189	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.516	-	-
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
2017-03-02	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-20	Niels_Mache_Nextcloud	SuperDry3	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-X	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-X	1000000	100000000						3	0.139
2019-03-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-10	Niels_Mache_Nextcloud	SuperDry3	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-X	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
2019-07-20	Niels_Mache_Nextcloud	SuperDry3	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
2019-08-11	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	SuperDry-Y	1000000	100000000						3	0.139
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	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	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M101341

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

1537187248608673

21633883830589081985481137

F8D9ED16B6341403

2017-09-21

Oliver Kruse

Manual testing

1537187248608673

21633883830589081985481137

F8D9ED16B6341403

2017-09-22

Oliver Kruse

Manual testing

1537187248608673

21633883830589081985481137

F8D9ED16B6341403

2017-11-06

kkmrkkblmbrbk

c4.xlarge

1537187248608673

21633883830589081985481137

F8D9ED16B63414__

2020-04-17

Oliver Kruse

AddPrpType5

1537187248608673

21633883830589081985481137

6ADFFFF6AE0E80__

2022-04-15

LordJulius

WhiteBox

1537187248608673

21633883830589081985481137

6ADFFFF6AE0E807A

2022-10-27

LordJulius

WhiteBox

1537187248608673

21633883830589081985481137

6ADFFFF6AE0E807A

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 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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: 67.7

ECM T-Level=30.76 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-03-23T17:39:31+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