M100 549 Mersenne number exponent details

is 2 ¹⁰⁰⁵⁴⁹ - 1

has 30269 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	295.5168	74.6269%	1000000000	6734439121410	1,185.3149	25.4904%	1,480.8317	81.0946%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1523%	0.0000	62.9680%
Difference	+23	+295.5168	+13.2632%	+999998800	+6734439103410	+1,185.3149	+21.3380%	+1,480.8316	+18.1266%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100549	29859665209791451523456393	26	84.626	148483153536044374004 2² × 23 × 654110767 × 2467391461	2009-03-18	654110767	2467391461	71,722,148	2.4260	4.2895

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	-	-	4.288%
2002-06-02	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.001	-	-	1.315%
2002-07-20	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.001	-	-	1.924%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.003	-	-	2.661%
2003-09-21	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.005	-	-	3.516%
2003-11-28	eteo	v4_computers	10000000	1000000000		-		-	-	0.206	-	-	9.560%
2016-10-31	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-		-	-	0.656	-	-	11.728%
2021-12-17	Seth_Tr	Manual testing	1000000000	6734439121410		-	skipped known factor: 29859665209791451523456393	-	-	1,185	-	-	25.490%

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	-	-
2002-04-14	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	-	-
2009-01-04	Sturle Sunde	ginglo.ifi	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2009-01-22	Sturle Sunde	gonzo.ifi	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		-	-	3.055	-	-
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:	11.208 GHz-days
Estimated T-Level:	30.701

Digits	B1	Complete	FacMiss
20	11000	65.490	0.000%
25	50000	10.983	0.002%
30	250000	1.379	25.171%
35	1000000	0.140	86.921%
40	3000000	0.012	98.805%

ECM Summary

B1	B2	factor	curves	GHz-days
		29859665209791451523456393	1	0.00000e+0
50000	5000000		8	0.019
250000	25000000		508	5.897
1000000	100000000		114	5.293

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-18	eteo	stephanie			29859665209791451523456393	84.626		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
2017-01-24	kkmrkkblmbrbk	kel1	250000	25000000						501	5.815
2019-01-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry-JP	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
2019-03-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-29	Niels_Mache_Nextcloud	SuperDry-JP	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	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
2019-09-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	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:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Robert Clark		28105BE476B2AC7E	0.000

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Doppelherz

29859665209791451523456393

18158CC29FDA88__

2017-09-21

Oliver Kruse

Manual testing

29859665209791451523456393

18158CC29FDA88__

2017-09-22

Oliver Kruse

Manual testing

29859665209791451523456393

18158CC29FDA88__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

29859665209791451523456393

18158CC29FDA88__

2020-04-17

Oliver Kruse

AddPrpType5

29859665209791451523456393

CBFB0791BF8377__

2022-04-15

LordJulius

WhiteBox

29859665209791451523456393

CBFB0791BF837775

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 = 6734439121410 (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 = 10000000, B2 = 1000000000 (P-1 stage 2)

B1 = 10000000 (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)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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

2⁵⁶

2⁵⁵

2⁵⁴

2⁵³

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=30.7 ~= 85-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