M2 564 381 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	11.5872	67.1642%	225000	238697550	1.3293	7.1918%	12.9165	69.5257%
Target	2⁶³	0.6224	65.0794%	12000	180000	0.0021	1.4797%	0.6245	65.5961%
Difference	+4	+10.9648	+2.0848%	+213000	+238517550	+1.3272	+5.7121%	+12.2920	+3.9296%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2564381	80808894662406310913	20	66.131	15756023512576 2⁹ × 211 × 145845893	2010-05-12	512	145845893	9.791	0.7992	1.4926
2564381	7046354224117302676999	22	72.577	1373889883000479 3 × 13 × 156631 × 224910431	2023-01-25	156631	224910431	453.58	1.2473	2.3018

exponent	prime factors	composite factor	digits	bits*
2564381	80808894662406310913 7046354224117302676999	569408096250696862575305309149126807790087	42	138.709

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.885%
2023-01-25	USAFSS	USAFSACS	225000	238697550			7046354224117302676999	22	72.577	1.329	0.356	2.659	7.192%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15	foxkid	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2022-03-11	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.060	-	-
2009-02-01	Sturle Sunde	gowin.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-

ECM factoring results:

Total ECM effort:	0.277 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		80808894662406310913	1	0.00000e+0
50000	5000000		3	0.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-17	Aca Arsov	backo6400	50000	5000000						3	0.277
2010-05-12	James Classen	towerofart			80808894662406310913	66.131		1		1	-

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Joe Decker		627E0CF183B66F0B	0.178
1999-03-26	foxkid	v4_computers	627E0CF183B66F0B	0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15

Oliver Kruse

GTX-3

80808894662406310913

F8CE288BD1EC7C__

2017-12-01

kkmrkkblmbrbk

c4.xlarge

80808894662406310913

F8CE288BD1EC7C__

2023-01-25

LordJulius

WhiteBox

80808894662406310913

7046354224117302676999

F8CE288BD1EC7CC2

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 = 225000, B2 = 238697550 (P-1 stage 2)

B1 = 225000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶¹

2⁶⁰

2⁵⁹

this exponent TF target: 63

TF double-checked to: 67.7

ECM T-Level=0.58 ~= -15-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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