M4 178 491 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	7.1112	67.1642%	337000	227966310	2.3038	8.0366%	9.4149	69.8030%
Target	2⁶⁵	1.7460	66.1538%	22000	450000	0.0082	1.8731%	1.7542	66.7878%
Difference	+2	+5.3651	+1.0103%	+315000	+227516310	+2.2956	+6.1635%	+7.6607	+3.0152%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4178491	10730364889	11	33.321	1284 2² × 3 × 107	-	4	107	3.500e-10	1.738e-6	1.909e-6
4178491	1612028399873	13	40.552	192896 2⁷ × 11 × 137	2008-09-30	128	137	6.143e-8	2.324e-5	4.711e-5
4178491	561912482919227167921	21	68.929	67238685319560 2³ × 3 × 5 × 39133 × 14318411	2023-01-20	39133	14318411	17.795	0.1478	0.2635

exponent	prime factors	composite factor	digits	bits*
4178491	10730364889 1612028399873	17297652942068091259097	23	73.873
4178491	10730364889 561912482919227167921	6029525977407287425674405525769	31	102.250
4178491	1612028399873 561912482919227167921	905818880708946215409479106074033	33	109.481
4178491	10730364889 1612028399873 561912482919227167921	9719767113352555898019305357595910337827337	43	142.802

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2023-01-20	USAFSS	6917th_Scty_Sq	337000	227966310			561912482919227167921	21	68.929	2.304	1.042	4.608	8.037%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30	markr	Manual testing	?	?	1612028399873	40.552	13	2.63744e-8	2.797	1.41526e-7

ECM factoring results:

Total ECM effort:	0.545 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
50000	5000000		3	0.545

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-12-02	rucio		50000	5000000						3	0.545

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20

kkmrkkblmbrbk

Manual testing

10730364889

1612028399873

670315C7730B03__

2018-01-17

Oliver Kruse

GTX-7

10730364889

1612028399873

670315C7730B03__

2023-01-27

Perig

brusaire

10730364889

1612028399873

561912482919227167921

68EDA48090A16EA6

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)

10⁰

10¹

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10³

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10¹

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10³

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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