M101 281 Mersenne number exponent details

is 2 ¹⁰¹²⁸¹ - 1

has 30489 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	293.3810	74.6269%	1000000000	6735532633830	1,185.5068	25.4993%	1,478.8878	81.0968%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1591%	0.0000	62.9706%
Difference	+23	+293.3809	+13.2632%	+999998800	+6735532615830	+1,185.5068	+21.3402%	+1,478.8878	+18.1263%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101281	529902193	9	28.981	2616 2³ × 3 × 109	-	8	109	5.530e-10	4.351e-8	5.246e-8
101281	312978236274852462332591	24	78.050	1545098469973896695 5 × 11 × 13 × 149 × 646619 × 22429283	2010-04-20	646619	22429283	726,746	0.0059	0.0074

exponent	prime factors	composite factor	digits	bits*
101281	529902193 312978236274852462332591	165847853763316470541489866272063	33	107.032

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: 529902193 skipped known factor: 312978236274852462332591	-	-	0.656	-	-	11.734%
2021-12-18	Seth_Tr	Manual testing	1000000000	6735532633830		-	skipped known factor: 529902193 skipped known factor: 312978236274852462332591	-	-	1,186	-	-	25.499%

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	529902193	28.981	9	5.53009e-10	0.000	1.17962e-9
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		-	-	0.379	-	-
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		-	-	3.033	-	-
2022-12-08	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.69	-	-
2022-12-08	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.38	-	-

ECM factoring results:

Total ECM effort:	12.574 GHz-days
Estimated T-Level:	30.756

Digits	B1	Complete	FacMiss
20	11000	82.105	0.000%
25	50000	12.904	0.000%
30	250000	1.543	21.378%
35	1000000	0.151	85.972%
40	3000000	0.013	98.746%

ECM Summary

B1	B2	factor	curves	GHz-days
		312978236274852462332591	1	0.00000e+0
50000	5000000		271	0.629
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			312978236274852462332591	78.050		1		1	-
2014-04-11	TJAOI	Manual testing	50000	5000000						39	0.091
2014-05-13	TJAOI	Manual testing	50000	5000000						231	0.536
2017-02-27	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-07	Niels_Mache_Nextcloud	SuperDry-JP	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
2019-02-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-21	storm5510	3570_Ivy_Bridge	1000000	100000000						3	0.139
2019-03-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-04	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
2019-05-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-17	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-27	Niels_Mache_Nextcloud	SuperDry3	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
2019-08-18	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
2019-09-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-24	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
2019-10-16	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-31	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 M101281

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

529902193

312978236274852462332591

43300635E96CC0__

2017-09-21

Oliver Kruse

Manual testing

529902193

312978236274852462332591

43300635E96CC0__

2017-10-13

kkmrkkblmbrbk

Manual testing

529902193

312978236274852462332591

43300635E96CC0__

2020-04-17

Oliver Kruse

AddPrpType5

529902193

312978236274852462332591

538DA1420C4F3A__

2022-04-15

LordJulius

WhiteBox

529902193

312978236274852462332591

538DA1420C4F3AF9

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

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10¹²

10¹³

TF factor-bounds graph:

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