M100 493 Mersenne number exponent details

is 2 ¹⁰⁰⁴⁹³ - 1

has 30252 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	295.6815	74.6269%	1000000000	6746801631570	1,187.4852	25.4924%	1,483.1666	81.0951%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1518%	0.0000	62.9678%
Difference	+23	+295.6814	+13.2632%	+999998800	+6746801613570	+1,187.4852	+21.3406%	+1,483.1666	+18.1273%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100493	2411833	7	21.202	12 2² × 3	-	4	4	2.787e-12	1.289e-8	2.623e-8
100493	7235497	7	22.787	36 2² × 3²	2008-07-26	9	9	5.603e-12	2.900e-8	5.902e-8
100493	91180315096903	14	46.374	453665007 3² × 43 × 1172261	2008-07-26	43	1172261	0.0002	0.0002	0.0004

exponent	prime factors	composite factor	digits	bits*
100493	2411833 7235497	17450810436001	14	43.988
100493	2411833 91180315096903	219911692901108853199	21	67.575
100493	7235497 91180315096903	659734896342696365791	21	69.160
100493	2411833 7235497 91180315096903	1591170394250894403994804903	28	90.362

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: 2411833 skipped known factor: 7235497 skipped known factor: 91180315096903	-	-	0.656	-	-	11.728%
2021-12-17	Seth_Tr	Manual testing	1000000000	6746801631570		-	skipped known factor: 2411833 skipped known factor: 7235497 skipped known factor: 91180315096903	-	-	1,187	-	-	25.492%

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	?	?	7235497	22.787	7	4.33260e-14	0.000	9.24988e-14
2008-07-26	J Feitsma	Manual testing	?	?	91180315096903	46.374	14	8.29259e-5	0.000	0.000
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.185	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	2411833 7235497	43.988	14	1.75665e-5	0.000	3.56691e-5
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	2411833	21.202	7	2.78730e-12	0.000	5.95075e-12
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	7235497	22.787	7	5.60349e-12	0.000	1.19632e-11
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	91180315096903	46.374	14	0.000	0.000	0.000
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		-	-	1.528	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.057	-	-
2022-10-13	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.77	-	-
2022-10-13	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.54	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.18	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.36	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.7	-	-

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	6.790
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
2014-05-19	TJAOI	Manual testing	50000	5000000						231	0.536
2017-01-21	kkmrkkblmbrbk	kel1	250000	25000000						585	6.790
2019-01-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-JP	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-JP	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-JP	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-JP	1000000	100000000						3	0.139
2019-04-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-29	J.R. Allen	lapdell	1000000	100000000						3	0.139
2019-05-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-04	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
2019-08-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-13	Niels_Mache_Nextcloud	SuperDry3	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
2019-09-04	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
2019-09-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100493

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

2411833

7235497

91180315096903

D6867AA3A52888__

2017-09-21

Oliver Kruse

Manual testing

2411833

7235497

91180315096903

D6867AA3A52888__

2017-09-22

Oliver Kruse

Manual testing

2411833

7235497

91180315096903

D6867AA3A52888__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

2411833

7235497

91180315096903

D6867AA3A52888__

2020-04-17

Oliver Kruse

AddPrpType5

2411833

7235497

91180315096903

59196DF0ABE436__

2022-04-15

LordJulius

WhiteBox

2411833

7235497

91180315096903

59196DF0ABE4369E

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 = 6746801631570 (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: 2023-03-23T17:39:31+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