M100 999 Mersenne number exponent details

is 2 ¹⁰⁰⁹⁹⁹ - 1

has 30404 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	294.2001	74.6269%	1000000000	6555983173740	1,153.9859	25.4558%	1,448.1861	81.0858%
Target	2⁴⁴	0.0000	61.3636%	1200	144000	0.0000	4.1565%	0.0001	62.9696%
Difference	+23	+294.2001	+13.2632%	+999998800	+6555983029740	+1,153.9859	+21.2993%	+1,448.1860	+18.1163%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100999	2510633143	10	31.225	12429 3² × 1381	-	9	1381	4.788e-9	2.699e-7	4.527e-7
100999	7141033297	10	32.733	35352 2³ × 3² × 491	2008-07-26	9	491	9.358e-9	1.136e-7	1.624e-7
100999	47875343983	11	35.479	237009 3 × 199 × 397	2008-07-26	199	397	5.895e-8	6.760e-7	1.305e-6

exponent	prime factors	composite factor	digits	bits*
100999	2510633143 7141033297	17928514870714762471	20	63.959
100999	2510633143 47875343983	120197425336245428569	21	66.704
100999	7141033297 47875343983	341879425487931601951	21	68.212
100999	2510633143 7141033297 47875343983	858333816539800026375264061993	30	99.437

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: 2510633143 skipped known factor: 7141033297 skipped known factor: 47875343983	-	-	0.656	-	-	11.732%
2021-12-18	Seth_Tr	Manual testing	1000000000	6555983173740		-	skipped known factor: 2510633143 skipped known factor: 7141033297 skipped known factor: 47875343983	-	-	1,154	-	-	25.456%

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	?	?	47875343983	35.479	11	1.36256e-8	0.000	2.90683e-8
2008-07-26	J Feitsma	Manual testing	?	?	7141033297	32.733	10	3.69334e-9	0.000	7.88050e-9
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	2510633143	31.225	10	4.78773e-9	0.000	1.02157e-8
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	47875343983	35.479	11	5.89463e-8	0.000	1.25753e-7
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	7141033297	32.733	10	9.35843e-9	0.000	1.99681e-8
2018-11-02	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.760	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.760	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.521	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.041	-	-
2022-11-04	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.72	-	-
2022-11-04	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.44	-	-
2022-11-04	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	36.99	-	-
2022-11-04	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	73.99	-	-
2022-11-04	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.0	-	-

ECM factoring results:

Total ECM effort:	12.597 GHz-days
Estimated T-Level:	30.756

Digits	B1	Complete	FacMiss
20	11000	82.490	0.000%
25	50000	12.939	0.000%
30	250000	1.545	21.330%
35	1000000	0.151	85.963%
40	3000000	0.013	98.746%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	0.652
250000	25000000	585	6.791
1000000	100000000	111	5.154

	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
2014-07-03	TJAOI	Manual testing	50000	5000000						231	0.536
2017-02-12	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-25	Niels_Mache_Nextcloud	SuperDry-JP	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	SuperDry3	1000000	100000000						3	0.139
2019-02-18	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-13	storm5510	7700_Kaby_Lake	1000000	100000000						3	0.139
2019-03-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-16	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-07	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-29	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-01-16	ANONYMOUS	v4_computers	3F2C3F96C7E16C__	0.000

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

2510633143

7141033297

47875343983

824E1694F9DC9F__

2017-09-21

Oliver Kruse

Manual testing

2510633143

7141033297

47875343983

824E1694F9DC9F__

2017-10-13

kkmrkkblmbrbk

Manual testing

2510633143

7141033297

47875343983

824E1694F9DC9F__

2020-04-17

Oliver Kruse

AddPrpType5

2510633143

7141033297

47875343983

0003720F61F7B6__

2022-04-15

LordJulius

WhiteBox

2510633143

7141033297

47875343983

0003720F61F7B6A5

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 = 6555983173740 (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=30.76 ~= 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