M100 829 Mersenne number exponent details

is 2 ¹⁰⁰⁸²⁹ - 1

has 30353 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	294.6961	74.6269%	1000000000	6548899577220	1,152.7424	25.4522%	1,447.4385	81.0849%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1549%	0.0000	62.9690%
Difference	+23	+294.6961	+13.2632%	+999998800	+6548899559220	+1,152.7424	+21.2973%	+1,447.4385	+18.1159%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100829	20165801	8	24.265	100 2² × 5²	-	25	25	2.265e-11	8.056e-8	1.639e-7
100829	133519173407	12	36.958	662107 662107	2008-07-26	1	662107	1.192e-7	0.0001	0.0002
100829	455856239755545392737	21	68.627	2260541311306992 2⁴ × 3² × 7 × 17 × 131917676897	2008-10-16	17	131917676897	623.49	23.159	43.254

exponent	prime factors	composite factor	digits	bits*
100829	20165801 133519173407	2692521080610054007	19	61.224
100829	20165801 455856239755545392737	9192706215518617036401187337	28	92.893
100829	133519173407 455856239755545392737	60865548324583632582711421344959	32	105.585
100829	20165801 133519173407 455856239755545392737	1227402535269436942520074563269595547159	40	129.851

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: 20165801 skipped known factor: 133519173407	-	-	0.656	-	-	11.731%
2021-12-17	Seth_Tr	Manual testing	1000000000	6548899577220		-	skipped known factor: 20165801 skipped known factor: 133519173407 skipped known factor: 455856239755545392737	-	-	1,153	-	-	25.452%

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	?	?	133519173407	36.958	12	2.84371e-8	0.000	6.06660e-8
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	133519173407	36.958	12	1.19231e-7	0.000	2.54361e-7
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	20165801	24.265	8	2.26463e-11	0.000	4.83308e-11
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	-	-
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		-	-	74.11	-	-
2022-10-25	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.2	-	-

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	factor	curves	GHz-days
		455856239755545392737	1	0.00000e+0
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
2008-10-16	ANONYMOUS	Manual testing			455856239755545392737	68.627		1		1	-
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
2017-02-07	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-X	1000000	100000000						3	0.139
2019-02-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-12	Niels_Mache_Nextcloud	SuperDry-X	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-JP	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-JP	1000000	100000000						3	0.139
2019-03-12	Niels_Mache_Nextcloud	SuperDry-JP	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	SuperDry-X	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
2019-04-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-02	Niels_Mache_Nextcloud	SuperDry-X	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
2019-06-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-01	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-01	Niels_Mache_Nextcloud	SuperDry3	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	SuperDry-Y	1000000	100000000						3	0.139
2019-09-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-06	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-13	Niels_Mache_Nextcloud	SuperDry3	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
2019-11-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100829

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Doppelherz

20165801

133519173407

455856239755545392737

7AD9D1EFDE84C2CE

2017-09-21

Oliver Kruse

Manual testing

20165801

133519173407

455856239755545392737

7AD9D1EFDE84C2CE

2017-09-22

Oliver Kruse

Manual testing

20165801

133519173407

455856239755545392737

7AD9D1EFDE84C2CE

2017-11-06

kkmrkkblmbrbk

c4.xlarge

20165801

133519173407

455856239755545392737

7AD9D1EFDE84C2__

2020-04-17

Oliver Kruse

AddPrpType5

20165801

133519173407

455856239755545392737

E79D38BE2DE4B6__

2022-04-15

LordJulius

WhiteBox

20165801

133519173407

455856239755545392737

E79D38BE2DE4B694

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 = 6548899577220 (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