M7 939 039 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷¹	60.2187	67.6056%	3000000	8070112050	146.8224	11.8779%	207.0411	71.4534%
Target	2⁶⁷	3.7428	65.6716%	55000	6000000	0.1257	2.5637%	3.8685	66.5517%
Difference	+4	+56.4759	+1.9340%	+2945000	+8064112050	+146.6967	+9.3142%	+203.1726	+4.9017%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7939039	3497117196535134051953	22	71.567	220248143165384 2³ × 5939 × 4635631907	2023-06-13	5939	4635631907	114.77	83.799	156.51
7939039	3797339508866849346417359854376591238871	40	131.480	239156118824132829327161628402165 3 × 5 × 7 × 43 × 71 × 106949 × 817711 × 1799599 × 4740379181	2023-06-13	1799599	4740379181	2.076e+10	86.255	160.05

exponent	prime factors	composite factor	digits	bits*
7939039	3497117196535134051953 3797339508866849346417359854376591238871	13279741297540539001718642201965564624051777016165 038347065063	62	203.047

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-06-15	MarkS	v4_computers	45000	697500		-		-	-	0.027	-	-	1.259%
2012-09-06	Squeeky_Squirrel	T7500_2200	100000	1900000		-		-	-	0.066	-	-	1.993%
2016-10-08	Squeeky_Squirrel	i5-5250U_1600	245000	6308750	12	-		-	-	0.191	-	-	3.102%
2023-06-13	Tha	Z-170	3000000	8070112050			3497117196535134051953 3797339508866849346417359854376591238871	62	203.047	146.8	3.633	293.6	11.878%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-09	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.077	-	-
1998-08-24	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.201	-	-
2013-10-02	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.247	-	-
2014-01-04	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.471	-	-
2015-06-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.941	-	-
2016-08-18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	1.883	-	-
2018-07-24	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	3.765	-	-
2020-02-07	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	7.530	-	-
2020-09-26	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	15.06	-	-
2021-12-04	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	30.12	-	-

ECM factoring results:

Total ECM effort:	2.088 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	2.088

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-01-27	Florimond C.	ichthys2	50000	5000000						3	1.044
2018-10-21	nranks	wlaptop	50000	5000000						3	1.044

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-31	ANONYMOUS	v4_computers	6377DF23F2EDF76A	1.817
2000-08-24	ANONYMOUS	v4_computers	6377DF23F2EDF76A	1.817
2002-06-23	MarkS	v4_computers	6377DF23F2EDF76A	1.817

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 = 3000000, B2 = 8070112050 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 245000, B2 = 6308750 (P-1 stage 2)

B1 = 245000 (P-1 stage 1)

B1 = 100000, B2 = 1900000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 45000, B2 = 697500 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

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