M2 725 699 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	10.9014	67.1642%	288000	226423890	1.4121	7.4782%	12.3135	69.6197%
Target	2⁶³	0.5855	65.0794%	14000	240000	0.0029	1.7061%	0.5885	65.6752%
Difference	+4	+10.3158	+2.0848%	+274000	+226183890	+1.4091	+5.7721%	+11.7250	+3.9445%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2725699	23854000933528634857	20	64.371	4375758462972 2² × 3 × 13 × 947 × 29619571	2009-03-10	947	29619571	1.9147	0.1808	0.3376
2725699	322809710977562804087	21	68.129	59215949922857 7 × 13 × 191837 × 3392071	2023-01-26	191837	3392071	24.227	0.0410	0.0437

exponent	prime factors	composite factor	digits	bits*
2725699	23854000933528634857 322809710977562804087	7700303147010891936158229456318050260559	40	132.500

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.298%
2003-11-28	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.932%
2023-01-26	USAFSS	USAFSACS	288000	226423890			322809710977562804087	21	68.129	1.412	0.421	2.824	7.478%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-29	Sturle Sunde	gimo.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-

ECM factoring results:

Total ECM effort:	0.311 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
		23854000933528634857	1	0.00000e+0
50000	5000000		3	0.311

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-10	S36049	Wolle3			23854000933528634857	64.371		1		1	-
2018-11-25	rucio		50000	5000000						3	0.311

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Jeremy Edward		3D1D6B1EC196ACB2	0.211
1999-04-23	Dry Creek Photo	v4_computers	3D1D6B1EC196ACB2	0.211

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-20

Oliver Kruse

GTX-3

23854000933528634857

8FE579A071644B__

2017-12-05

kkmrkkblmbrbk

c4.xlarge

23854000933528634857

8FE579A071644B__

2023-01-27

LordJulius

WhiteBox

23854000933528634857

322809710977562804087

8FE579A071644B97

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 = 288000, B2 = 226423890 (P-1 stage 2)

B1 = 288000 (P-1 stage 1)

B1 = 15000, B2 = 225000 (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

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