M100 547 Mersenne number exponent details

is 2 ¹⁰⁰⁵⁴⁷ - 1

has 30268 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	295.5227	74.6269%	1000000000	6547395855000	1,152.4784	25.4485%	1,448.0010	81.0840%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1523%	0.0000	62.9679%
Difference	+23	+295.5226	+13.2632%	+999998800	+6547395837000	+1,152.4784	+21.2962%	+1,448.0010	+18.1160%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100547	1619316206987851903	19	60.490	8052533675733 3 × 47 × 57110167913	2014-04-23	47	57110167913	1.6575	10.026	18.726
100547	86418211677568295856841399	26	86.160	429740378517351566217 3 × 7 × 313 × 1097 × 4230419 × 14088103	2014-06-02	4230419	14088103	309,598,897	0.0154	0.0277

exponent	prime factors	composite factor	digits	bits*
100547	1619316206987851903 86418211677568295856841399	139938410748393183012328596847059985571332297	45	146.650

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: 86418211677568295856841399	-	-	0.656	-	-	11.728%
2021-12-17	Seth_Tr	Manual testing	1000000000	6547395855000		-	skipped known factor: 1619316206987851903 skipped known factor: 86418211677568295856841399	-	-	1,152	-	-	25.449%

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		-	-	0.185	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷		-	-	0.191	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.764	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.764	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹	1619316206987851903	60.490	19	0.130	0.000	0.264
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.055	-	-
2022-10-23	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.76	-	-
2022-10-23	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.53	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.16	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.32	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.6	-	-

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
		86418211677568295856841399	1	0.00000e+0
50000	5000000		281	0.652
250000	25000000		585	6.790
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
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2014-04-11	TJAOI	Manual testing	50000	5000000						40	0.093
2014-06-02	TJAOI	Manual testing	50000	5000000						231	0.536
2014-06-02	TJAOI	Manual testing			86418211677568295856841399	86.160		1		1	-
2017-01-25	kkmrkkblmbrbk	kel1	250000	25000000						585	6.790
2019-01-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-15	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-27	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100547

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Ollaptop

1619316206987851903

86418211677568295856841399

8B9EC97F5D4E035B

2017-09-21

Oliver Kruse

Manual testing

1619316206987851903

86418211677568295856841399

8B9EC97F5D4E035B

2017-09-22

Oliver Kruse

Manual testing

1619316206987851903

86418211677568295856841399

8B9EC97F5D4E035B

2017-11-06

kkmrkkblmbrbk

c4.xlarge

1619316206987851903

86418211677568295856841399

8B9EC97F5D4E03__

2020-04-17

Oliver Kruse

AddPrpType5

1619316206987851903

86418211677568295856841399

EB9E293FEE311A__

2022-04-15

LordJulius

WhiteBox

1619316206987851903

86418211677568295856841399

EB9E293FEE311AC2

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 = 6547395855000 (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: 2023-03-25T13:08:14+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