M7 456 177 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	2⁷²	128.2606	68.0556%	3100000	11007976980	190.5545	11.3785%	318.8150	71.6904%
Target	2⁶⁷	3.9851	65.6716%	50000	8800000	0.1665	2.4350%	4.1517	66.5076%
Difference	+5	+124.2754	+2.3839%	+3050000	+10999176980	+190.3879	+8.9435%	+314.6634	+5.1828%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7456177	37308714773258521252634260003317529	35	114.845	2501866222680773354269504332 2² × 3 × 47 × 163 × 13499 × 75161 × 2597303 × 10327153	2023-04-30	2597303	10327153	2.138e+10	0.9544	1.6713
7456177	4171412792125068067861031601356461034633	40	131.616	279728659346811916338696868472708 2² × 41 × 59 × 151 × 653 × 1187 × 331651 × 2108123 × 353283211	2023-04-30	2108123	353283211	1.802e+10	6.7160	11.367

exponent	prime factors	composite factor	digits	bits*
7456177	37308714773258521252634260003317529 4171412792125068067861031601356461034633	15563005006291610394731218484540832807497273178385 0827803758825399764981857	75	246.461

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-22	ANONYMOUS	v4_computers	40000	520000		-		-	-	0.021	-	-	0.961%
2012-07-03	Nesowa	EPC	90000	1665000		-		-	-	0.056	-	-	1.647%
2019-08-26	harlee	i5-5250U_1600	440000	13530000	12	-		-	-	0.365	-	-	3.550%
2023-04-30	DRobinsonPE	5500X	3100000	11007976980			37308714773258521252634260003317529 4171412792125068067861031601356461034633	75	246.461	190.6	3.252	381.1	11.379%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-06	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.214	-	-
2013-10-24	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.263	-	-
2013-11-25	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.501	-	-
2015-06-21	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.002	-	-
2016-05-22	america64	Manual testing	2⁶⁶	2⁶⁷		-	-	2.004	-	-
2016-06-19	america64	Manual testing	2⁶⁷	2⁶⁸		-	-	4.009	-	-
2017-09-21	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	8.018	-	-
2017-09-21	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	16.04	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	32.07	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	64.14	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-12-06	Donna Noble	3570K-black	50000	5000000						3	0.995
2018-02-13	arnaud	snd-15-157	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-12	curtisc	v4_computers	0645110B74B5D23A	1.626
2002-01-28	ANONYMOUS	v4_computers	0645110B74B5D23A	1.626

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-04-30

retsu

pritchett

37308714773258521252634260003317529

4171412792125068067861031601356461034633

97EE48ADBBD034__

2023-05-01

Naegi Makoto

5950X

37308714773258521252634260003317529

4171412792125068067861031601356461034633

97EE48ADBBD0340F

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 = 3100000, B2 = 11007976980 (P-1 stage 2)

B1 = 3100000 (P-1 stage 1)

B1 = 440000, B2 = 13530000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 90000, B2 = 1665000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 40000, B2 = 520000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

this exponent TF target: 67

TF double-checked to: 67.9

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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