M4 174 409 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	7.1181	67.1642%	200000	108185220	1.1002	6.7243%	8.2183	69.3722%
Target	2⁶⁵	1.7477	66.1538%	22000	450000	0.0082	1.8727%	1.7559	66.7877%
Difference	+2	+5.3704	+1.0103%	+178000	+107735220	+1.0920	+4.8516%	+6.4624	+2.5845%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4174409	133581089	9	26.993	16 2⁴	-	16	16	2.149e-12	2.894e-6	5.889e-6
4174409	35956900979889847	17	54.997	4306825347 3 × 11 × 43 × 3035113	2014-12-30	43	3035113	0.0007	0.0299	0.0559
4174409	10462110443544551449956322753	29	93.079	1253124746945561808864 2⁵ × 3² × 7 × 13 × 23 × 3847 × 137453 × 3931481	2023-01-12	137453	3931481	489,271,678	0.0622	0.0724

exponent	prime factors	composite factor	digits	bits*
4174409	133581089 35956900979889847	4803161989958852862303383	25	81.990
4174409	133581089 10462110443544551449956322753	1397540106286954202701694595781218017	37	120.072
4174409	35956900979889847 10462110443544551449956322753	376185069259202883852907159578674959119788791	45	148.076
4174409	133581089 35956900979889847 10462110443544551449956322753	50251211217184744497011854192416182216251868151773 399	53	175.069

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2023-01-12	USAFSS	6917th_Scty_Sq	200000	108185220			10462110443544551449956322753	29	93.079	1.100	1.041	2.200	6.724%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-12-30	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	35956900979889847	54.997	17	0.000	2.796	0.001

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

133581089

35956900979889847

9DC89836EC8572__

2018-01-15

ATH

ec2-1xf

133581089

35956900979889847

9DC89836EC8572__

2023-01-18

Perig

brollach

133581089

35956900979889847

10462110443544551449956322753

3A0B93B7F62704D5

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 = 200000, B2 = 108185220 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁵⁵

this exponent TF target: 65

TF double-checked to: 67.7

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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