M2 528 893 Mersenne number exponent details

is 2 ^2528893 - 1

has 761273 decimal digits

takes 0.175 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	2⁶⁹	47.2091	68.1159%	5000000	8646469650	47.8540	13.0599%	95.0632	72.2800%
Target	2⁶³	0.6311	65.0794%	11000	180000	0.0020	1.4349%	0.6331	65.5804%
Difference	+6	+46.5780	+3.0366%	+4989000	+8646289650	+47.8520	+11.6251%	+94.4300	+6.6996%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2528893	201011580987298260907384769595442924903	39	127.241	39742998416164357469332385671407 3 × 7 × 1613 × 208729 × 360277 × 3397967 × 4591646869	2023-02-06	3397967	4591646869	5.850e+10	25.483	46.992

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-06	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.453%
2011-03-17	James Heinrich	WHS	300000	8000000		-		-	-	0.072	-	-	3.566%
2018-01-03	Jocelyn Larouche	low 4M	2528893	16000000	12	-		-	-	0.328	-	-	5.114%
2022-09-15	seatsea	dt	3040000	7925689200		-		-	-	43.72	-	-	12.408%
2023-02-06	Architects Cubed	gpu72ng	5000000	8646469650			201011580987298260907384769595442924903	39	127.241	47.85	0.351	95.71	13.060%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-08-16	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31	Sturle Sunde	gehry.ifi	2⁶⁰	2⁶¹		-	-	0.061	-	-
2012-06-14	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-01-23	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.388	-	-
2015-02-23	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.776	-	-
2015-02-23	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.477	-	-
2015-11-08	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.955	-	-
2017-08-08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.910	-	-
2019-04-15	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.82	-	-
2021-06-10	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	23.64	-	-

ECM factoring results:

Total ECM effort:	16.543 GHz-days
Estimated T-Level:	23.159

Digits	B1	Complete	FacMiss
20	11000	6.821	0.109%
25	50000	0.632	53.161%
30	250000	0.040	96.087%
35	1000000	0.002	99.813%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	140	12.89
50000	5150000	7	0.653
50000	6750000	7	0.740
50000	6928440	7	0.750
50000	7000000	14	1.507

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-10	Carsten Kossendey	durandal	50000	5000000						1	0.092
2009-04-07	Carsten Kossendey	Manual testing	50000	5000000						1	0.092
2009-10-25	Piepen	T41-2000	50000	5000000						3	0.276
2011-10-12	Beat Bucheli	I7	50000	5000000						3	0.276
2013-10-04	arnaud	srv-630	50000	5000000						3	0.276
2015-06-13	guru	w6	50000	5000000						3	0.276
2016-02-23	S36049	Wolle4	50000	5000000						3	0.276
2016-05-31	lettp	Home	50000	5000000						3	0.276
2017-01-16	Bruce	eleven	50000	5000000						3	0.276
2017-07-20	Bruce	eleven	50000	5000000						3	0.276
2017-11-30	Yan Jinzhao	cndns	50000	5000000						3	0.276
2018-06-22	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2019-08-12	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2020-06-05	Keysarecool	HPLaptop	50000	5000000						3	0.276
2020-06-23	mnd9	office2	50000	5000000						3	0.276
2020-07-02	GAN	LMS-11	50000	5000000						3	0.276
2020-07-09	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.276
2020-07-15	daveward2005	Dave2	50000	5000000						3	0.276
2020-07-21	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.276
2020-07-27	GAN	LMS-06	50000	5000000						3	0.276
2020-08-04	J.R. Allen	lapasus	50000	5000000						3	0.276
2020-08-12	GAN	LMS-04	50000	5000000						3	0.276
2020-08-31	mnd9	libproj	50000	5000000						7	0.645
2020-10-02	mnd9	kitchen	50000	5000000						7	0.645
2020-10-29	Oliver Kruse	Krusen-NAS	50000	5000000						7	0.645
2021-01-11	Per Jessen	earth	50000	5000000						7	0.645
2021-02-06	Sergey Nosov	TS140-02	50000	5000000						7	0.645
2021-02-18	Zenzoma	AM3700X_1	50000	5000000						7	0.645
2021-03-06	mnd9	kitchen	50000	5000000						7	0.645
2021-04-12	Zenzoma	AMD3970X	50000	5000000						7	0.645
2021-06-02	kutens	arcturus	50000	5150000						7	0.653
2021-07-24	nordi	sweet16	50000	6750000						7	0.740
2021-09-12	Esti	Estis_CoreI7	50000	5000000						7	0.645
2022-02-02	daveward2005	d12436	50000	5000000						7	0.645
2022-03-29	carlos56	gjhl	50000	6928440						7	0.750
2022-09-09	Nesowa	entropy_generator_2	50000	7000000						7	0.754
2022-10-19	Alvin Bunk	BADCAT	50000	7000000						7	0.754
2023-01-10	daveward2005	Dave2	50000	5000000						8	0.737

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Michael B. Clark		D50F76E10362249F	0.175
2015-11-14	MadPoo	Manual testing	D50F76E10362249F	0.175

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-02-08

LordJulius

WhiteBox

201011580987298260907384769595442924903

45BF8172DD2058CE

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 = 5000000, B2 = 8646469650 (P-1 stage 2)

B1 = 3040000, B2 = 7925689200 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2528893, B2 = 16000000 (P-1 stage 2)

B1 = 3040000 (P-1 stage 1)

B1 = 2528893 (P-1 stage 1)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

this exponent TF target: 63

TF double-checked to: 67.7

ECM T-Level=23.16 ~= 60-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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