M6 940 589 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	137.7885	68.0556%	4000000	80000000	2.5739	6.1903%	140.3625	70.0330%
Target	2⁶⁷	4.2812	65.6716%	45000	900000	0.0290	2.2374%	4.3101	66.4397%
Difference	+5	+133.5074	+2.3839%	+3955000	+79100000	+2.5450	+3.9529%	+136.0523	+3.5933%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6940589	1301146677547045118373497	25	80.106	93734600733961132 2² × 11 × 41 × 47 × 812051 × 1361389	2021-11-17	812051	1361389	53,089	0.2662	0.5225

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-08	Fabrice Bellet	v4_computers	30000	30000		-		-	-	0.009	-	-	0.234%
2011-04-22	Carsten Kossendey	leela	440000	13310000		-		-	-	0.361	-	-	3.506%
2021-11-17	Seth_Tr	Manual testing	3000000	3000000			1301146677547045118373497	25	80.106	0.949	3.027	1.897	2.765%
2021-11-23	riccardo uberti	Colab_noGPU14	4000000	80000000		-	skipped known factor: 1301146677547045118373497	-	-	2.574	-	-	6.190%
2021-12-02	Seth_Tr	Manual testing	4000000	4000000			1301146677547045118373497	25	80.106	1.265	3.027	2.529	3.046%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-11-25	riccardo uberti	Colab_noGPU15	2000000	40000000	2	7			-	-	1.603
2021-11-30	riccardo uberti	Colab_noGPU15	2000000	40000000	6	5			-	-	1.603

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2004-10-18	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.283	-	-
2014-02-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.538	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.077	-	-
2016-04-05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.153	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.307	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.613	-	-
2021-07-28	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.23	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.45	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.91	-	-

ECM factoring results:

Total ECM effort:	8.407 GHz-days
Estimated T-Level:	3.654

Digits	B1	Complete	FacMiss
20	11000	0.731	48.154%
25	50000	0.070	93.271%
30	250000	0.004	99.554%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989
50000	14400000		10	6.417

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-10-21	Donna Noble	isk3225-test	50000	5000000						3	0.995
2017-04-12	ANONYMOUS		50000	5000000						3	0.995
2021-11-24	riccardo uberti	Colab_noGPU7	50000	14400000						10	6.417

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15	ANONYMOUS	v4_computers	69993C89B4867E20	1.513
2002-01-02	Fabrice Bellet	v4_computers	69993C89B4867E20	1.513

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 = 4000000, B2 = 80000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 440000, B2 = 13310000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

ECM T-Level=3.65 ~= -4-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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