M4 174 949 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	7.1172	67.1642%	337000	227966310	2.3038	8.0358%	9.4210	69.8028%
Target	2⁶⁵	1.7475	66.1538%	22000	450000	0.0082	1.8728%	1.7557	66.7877%
Difference	+2	+5.3697	+1.0103%	+315000	+227516310	+2.2956	+6.1630%	+7.6653	+3.0151%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4174949	6555823314094235063	19	62.507	785138131519 7 × 79 × 1419779623	2009-12-01	79	1419779623	0.2672	13.989	26.128
4174949	1213711806436894955844767	25	80.006	145356482969839267 7 × 577 × 210857 × 170676029	2023-01-25	210857	170676029	112,060	1.7177	3.1409

exponent	prime factors	composite factor	digits	bits*
4174949	6555823314094235063 1213711806436894955844767	7956880157230425429839548665186251836465321	43	142.513

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-03	Carsten Kossendey	leela	25000	337500		-		-	-	0.008	-	-	1.349%
2023-01-25	USAFSS	6917th_Scty_Sq	337000	227966310			1213711806436894955844767	25	80.006	2.304	1.041	4.608	8.036%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-24	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.074	-	-

ECM factoring results:

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		6555823314094235063	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-01	Aca Arsov	backo6400			6555823314094235063	62.507		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Dax Prather		F14D78F90B5DC2EF	0.521
1999-12-08	ANONYMOUS	v4_computers	F14D78F90B5DC2EF	0.521

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20

kkmrkkblmbrbk

Manual testing

6555823314094235063

BC8D555AF23C3D__

2018-01-16

Chang Chia-Tche

exbpc13

6555823314094235063

BC8D555AF23C3D__

2023-01-31

Perig

bruinneall

6555823314094235063

1213711806436894955844767

0F6EEC6826056A2C

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 = 337000, B2 = 227966310 (P-1 stage 2)

B1 = 337000 (P-1 stage 1)

B1 = 25000, B2 = 337500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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