M100 741 Mersenne number exponent details

is 2 ¹⁰⁰⁷⁴¹ - 1

has 30327 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	294.9536	74.6269%	1000000000	6547509398430	1,152.4983	25.4509%	1,447.4519	81.0845%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1541%	0.0000	62.9686%
Difference	+23	+294.9535	+13.2632%	+999998800	+6547509380430	+1,152.4983	+21.2967%	+1,447.4519	+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
100741	8907357655236967395952729	25	82.881	44209198118129497404 2² × 3 × 7 × 67 × 487 × 16129822476839	2009-03-22	487	16129822476839	14,318,773	2,831.7	5,288.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-11-25	ANONYMOUS	v4_computers	1000000	25000000		-		-	-	0.007	-	-	4.289%
2002-06-02	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.001	-	-	1.315%
2002-07-20	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.001	-	-	1.925%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.003	-	-	2.662%
2003-09-21	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.005	-	-	3.517%
2016-10-31	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-		-	-	0.656	-	-	11.730%
2021-12-17	Seth_Tr	Manual testing	1000000000	6547509398430		-		-	-	1,152	-	-	25.451%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-14	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.006	-	-
1999-12-30	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.012	-	-
2000-12-07	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.048	-	-
2000-12-07	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.095	-	-
2000-12-14	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.095	-	-
2002-04-20	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.191	-	-
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.185	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷		-	-	0.191	-	-
2022-03-07	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2009-01-05	Sturle Sunde	ginglo.ifi	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.381	-	-
2009-01-24	Sturle Sunde	gonzo.ifi	2⁵⁹	2⁶⁰		-	-	0.762	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.762	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.525	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.049	-	-
2022-10-24	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.74	-	-
2022-10-24	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.49	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.09	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.18	-	-
2022-10-24	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.4	-	-

ECM factoring results:

Total ECM effort:	11.229 GHz-days
Estimated T-Level:	30.701

Digits	B1	Complete	FacMiss
20	11000	65.937	0.000%
25	50000	11.019	0.002%
30	250000	1.381	25.131%
35	1000000	0.140	86.919%
40	3000000	0.012	98.805%

ECM Summary

B1	B2	factor	curves	GHz-days
		8907357655236967395952729	1	0.00000e+0
50000	5000000		22	0.051
250000	25000000		507	5.885
1000000	100000000		114	5.293

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22	eteo	stephanie			8907357655236967395952729	82.881		1		1	-
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-15	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-15	Rob_Dee	twopc	50000	5000000						4	0.009
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-01-16	Rob_Dee	twopc	250000	25000000						1	0.012
2010-04-19	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2010-05-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-05-22	Rob_Dee	twopc	50000	5000000						1	0.002
2010-05-23	Rob_Dee	twopc	50000	5000000						1	0.002
2017-02-02	kkmrkkblmbrbk	kel1	250000	25000000						499	5.792
2019-01-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-01-31	Niels_Mache_Nextcloud	SuperDry3	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-JP	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-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-JP	1000000	100000000						3	0.139
2019-03-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-19	Niels_Mache_Nextcloud	SuperDry3	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-X	1000000	100000000						3	0.139
2019-04-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-05-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-15	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-29	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-24	Niels_Mache_Nextcloud	SuperDry3	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	SuperDry3	1000000	100000000						3	0.139
2019-08-22	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
2019-09-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-28	Niels_Mache_Nextcloud	SuperDry-Y	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
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Robert Clark		56A9D344FA1DFB18	0.000

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

8907357655236967395952729

71D0D3DBB5C9E8__

2017-09-21

Oliver Kruse

Manual testing

8907357655236967395952729

71D0D3DBB5C9E8__

2017-09-22

Oliver Kruse

Manual testing

8907357655236967395952729

71D0D3DBB5C9E8__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

8907357655236967395952729

71D0D3DBB5C9E8__

2020-04-17

Oliver Kruse

AddPrpType5

8907357655236967395952729

CD268B2C69AC18__

2022-04-15

LordJulius

WhiteBox

8907357655236967395952729

CD268B2C69AC188B

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 = 6547509398430 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

B1 = 1000000, B2 = 25000000 (P-1 stage 2)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵³

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=30.7 ~= 85-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