M100 811 Mersenne number exponent details

is 2 ¹⁰⁰⁸¹¹ - 1

has 30348 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	294.7488	74.6269%	1000000000	6588272961270	1,159.6546	25.4609%	1,454.4033	81.0871%
Target	2⁴⁴	0.0000	61.3636%	1200	144000	0.0000	4.1548%	0.0001	62.9689%
Difference	+23	+294.7487	+13.2632%	+999998800	+6588272817270	+1,159.6546	+21.3061%	+1,454.4033	+18.1182%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100811	201623	6	17.621	1 1	-	1	1	1.732e-13	3.222e-9	6.558e-9
100811	1068798223	10	29.993	5301 3² × 19 × 31	2008-07-26	19	31	8.140e-10	6.333e-8	1.246e-7

exponent	prime factors	composite factor	digits	bits*
100811	201623 1068798223	215494304115929	15	47.615

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-10-31	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 201623 skipped known factor: 1068798223	-	-	0.656	-	-	11.730%
2021-12-16	Seth_Tr	Manual testing	1000000000	6588272961270		-	skipped known factor: 201623 skipped known factor: 1068798223	-	-	1,160	-	-	25.461%

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	?	?	1068798223	29.993	10	1.04576e-10	0.000	2.23185e-10
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	1068798223	29.993	10	8.14032e-10	0.000	1.73730e-9
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	201623	17.621	6	1.73242e-13	0.000	3.69732e-13
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	201623 1068798223	47.615	15	0.000	0.000	0.001
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.762	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.762	-	-
2018-11-29	ANONYMOUS	Manual testing	2⁶⁰	2⁶¹		-	-	1.524	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.524	-	-
2018-11-29	ANONYMOUS	Manual testing	2⁶¹	2⁶²		-	-	3.047	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.047	-	-
2022-10-25	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.74	-	-
2022-10-25	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.48	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.06	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.13	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.3	-	-

ECM factoring results:

Total ECM effort:	12.736 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.990	0.000%
25	50000	13.039	0.000%
30	250000	1.561	21.003%
35	1000000	0.153	85.797%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	0.652
250000	25000000	585	6.791
1000000	100000000	114	5.293

	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
2010-04-19	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-04-11	TJAOI	Manual testing	50000	5000000						38	0.088
2014-06-26	TJAOI	Manual testing	50000	5000000						231	0.536
2017-02-05	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-01-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-12	storm5510	3570_Ivy_Bridge	1000000	100000000						3	0.139
2019-03-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-01	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-08	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-21	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-13	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100811

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

201623

1068798223

70EF5DED395202__

2017-09-21

Oliver Kruse

Manual testing

201623

1068798223

70EF5DED395202__

2017-10-13

kkmrkkblmbrbk

Manual testing

201623

1068798223

70EF5DED395202__

2020-04-17

Oliver Kruse

AddPrpType5

201623

1068798223

44DA8F0C5BF676__

2022-04-15

LordJulius

WhiteBox

201623

1068798223

44DA8F0C5BF6762E

2022-05-12

Jorge Coveiro

Manual testing

201623

44DA8F0C5BF6762E

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 = 6588272961270 (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:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=30.77 ~= 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