M7 164 019 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	133.4912	68.0556%	3300000	8474534250	146.9722	11.1253%	280.4634	71.6095%
Target	2⁶⁷	4.1477	65.6716%	45000	5000000	0.0996	2.3086%	4.2472	66.4641%
Difference	+5	+129.3436	+2.3839%	+3255000	+8469534250	+146.8726	+8.8167%	+276.2161	+5.1453%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7164019	11539282238285595880498863247959432288833	41	133.084	805363737748713109254656028128864 2⁵ × 11 × 17 × 43 × 157 × 373 × 18119 × 260191 × 408809 × 27731707	2023-01-18	408809	27731707	1.929e+10	0.5999	0.8922

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-17	Todd	v4_computers	35000	35000		-		-	-	0.011	-	-	0.267%
2012-01-06	Carsten Kossendey	mother	455000	13991250		-		-	-	0.377	-	-	3.573%
2023-01-18	DRobinsonPE	5600G	3300000	8474534250			11539282238285595880498863247959432288833	41	133.084	147.0	3.124	293.9	11.125%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-07	Greg	v4_computers	2¹	2⁶²		-	-	0.086	-	-
2001-11-17	Todd	v4_computers	2¹	2⁶³		-	-	0.223	-	-
2014-02-02	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.274	-	-
2014-02-05	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.522	-	-
2015-06-21	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.043	-	-
2016-10-26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.086	-	-
2018-07-27	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.172	-	-
2020-05-15	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.345	-	-
2021-08-19	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	16.69	-	-
2021-08-31	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	33.38	-	-
2021-10-13	SRBase	Manual testing	2⁷¹	2⁷²		-	-	66.76	-	-

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
2012-10-30	Donna Noble	isk3225-test	50000	5000000						3	0.995
2017-10-21	arnaud	snd-15-157	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-29	Mats Dahlgren	v4_computers	105DAE33D3B11D38	1.562
2001-12-08	Todd	v4_computers	105DAE33D3B11D38	1.562

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 = 3300000, B2 = 8474534250 (P-1 stage 2)

B1 = 3300000 (P-1 stage 1)

B1 = 455000, B2 = 13991250 (P-1 stage 2)

B1 = 455000 (P-1 stage 1)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.9

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