M100 823 Mersenne number exponent details

is 2 ¹⁰⁰⁸²³ - 1

has 30351 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	294.7137	74.6269%	1000000000	6734439121410	1,185.3149	25.4936%	1,480.0285	81.0954%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1549%	0.0000	62.9689%
Difference	+23	+294.7137	+13.2632%	+999998800	+6734439103410	+1,185.3149	+21.3388%	+1,480.0285	+18.1265%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100823	43757183	8	25.383	217 7 × 31	-	7	31	4.642e-11	2.677e-8	4.590e-8
100823	32718508623684503	17	54.861	162257166637 23 × 7054659419	2010-02-07	23	7054659419	0.0438	1.2385	2.3131
100823	37591882852263463	17	55.061	186425135397 3² × 263 × 521 × 151171	2008-08-26	521	151171	0.0909	2.813e-5	4.957e-5

exponent	prime factors	composite factor	digits	bits*
100823	43757183 32718508623684503	1431669769333640932035049	25	80.244
100823	43757183 37591882852263463	1644914897281054314704729	25	80.444
100823	32718508623684503 37591882852263463	1229950343282319705821364346213889	34	109.922
100823	43757183 32718508623684503 37591882852263463	53819162251917284032131605006956498114687	41	135.305

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: 43757183 skipped known factor: 37591882852263463	-	-	0.656	-	-	11.731%
2021-12-18	Seth_Tr	Manual testing	1000000000	6734439121410		-	skipped known factor: 43757183 skipped known factor: 32718508623684503 skipped known factor: 37591882852263463	-	-	1,185	-	-	25.494%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	32718508623684503	54.861	17	0.044	0.000	0.089
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	37591882852263463	55.061	17	0.091	0.000	0.184
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	43757183	25.383	8	4.64182e-11	0.000	9.90642e-11
2018-12-03	ANONYMOUS	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-12-03	ANONYMOUS	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2018-12-03	ANONYMOUS	Manual testing	2⁵⁹	2⁶⁰		-	-	0.762	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.762	-	-
2018-12-03	ANONYMOUS	Manual testing	2⁶⁰	2⁶¹		-	-	1.523	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.523	-	-
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		-	-	19.47	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.06	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.12	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.2	-	-

ECM factoring results:

Total ECM effort:	12.734 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.951	0.000%
25	50000	13.036	0.000%
30	250000	1.560	21.008%
35	1000000	0.153	85.798%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	factor	curves	GHz-days
		32718508623684503	1	0.00000e+0
		37591882852263463	1	0.00000e+0
50000	5000000		280	0.650
250000	25000000		585	6.791
1000000	100000000		114	5.293

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			37591882852263463	55.061		1		1	-
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-01	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-02	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-03	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-04	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-04	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-04	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-04	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-05	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-05	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-05	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-05	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-05	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-06	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc			32718508623684503	54.861		1		1	-
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-07	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-08	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-08	Rob_Dee	twopc	50000	5000000						1	0.002
2010-02-08	Rob_Dee	twopc	50000	5000000						1	0.002
2010-04-19	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-06-26	TJAOI	Manual testing	50000	5000000						230	0.534
2017-02-06	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-25	Niels_Mache_Nextcloud	SuperDry3	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-X	1000000	100000000						3	0.139
2019-02-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-05-09	Niels_Mache_Nextcloud	SuperDry-X	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
2019-06-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-25	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	SuperDry3	1000000	100000000						3	0.139
2019-08-30	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	SuperDry3	1000000	100000000						3	0.139
2019-09-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-29	Niels_Mache_Nextcloud	SuperDry3	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	SuperDry3	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
2019-11-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100823

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

43757183

32718508623684503

37591882852263463

4DBBFB943B2C59F2

2017-09-21

Oliver Kruse

Manual testing

43757183

32718508623684503

37591882852263463

4DBBFB943B2C59F2

2017-09-22

Oliver Kruse

Manual testing

43757183

32718508623684503

37591882852263463

4DBBFB943B2C59F2

2017-11-06

kkmrkkblmbrbk

c4.xlarge

43757183

32718508623684503

37591882852263463

4DBBFB943B2C59__

2020-04-17

Oliver Kruse

AddPrpType5

43757183

32718508623684503

37591882852263463

E077C03AFFB04E__

2022-04-15

LordJulius

WhiteBox

43757183

32718508623684503

37591882852263463

E077C03AFFB04E89

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 = 6734439121410 (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: 67.7

ECM T-Level=30.77 ~= 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