M5 147 069 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	2⁷¹	92.8836	67.6056%	305000	9683750	0.1640	3.3138%	93.0476	68.6791%
Target	2⁶⁵	1.4174	64.6154%	36000	6400000	0.0769	2.5420%	1.4944	65.5149%
Difference	+6	+91.4662	+2.9902%	+269000	+3283750	+0.0871	+0.7718%	+91.5532	+3.1643%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5147069	76713320069606925349139475429733791189919	41	135.817	7452136358537929581781347348338811 3² × 23 × 181 × 467 × 929 × 1409 × 13499 × 16087 × 669091 × 2239373	2022-07-21	669091	2239373	3.253e+10	0.1517	0.2737

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-09-15	ANONYMOUS	v4_computers	20000	20000		-		-	-	0.004	-	-	0.184%
2009-09-24	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	1.416%
2019-05-09	harlee	P4_2600	305000	9683750	12	-		-	-	0.164	-	-	3.314%
2022-07-21	Sid & Andy	Magic_8_Ball	4000000	4000000			76713320069606925349139475429733791189919	41	135.817	0.804	1.427	1.608	3.235%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-12	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.060	-	-
2008-10-12	Sturle Sunde	rumblebuffin.ifi	2⁶¹	2⁶²		-	-	0.060	-	-
2009-11-14	S485122	USB-W	2⁶²	2⁶³		-	-	0.191	-	-
2014-12-16	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.381	-	-
2014-12-16	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.726	-	-
2015-08-07	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.452	-	-
2016-05-29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.904	-	-
2018-06-20	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.807	-	-
2020-10-12	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.61	-	-
2022-01-15	Gordon Spence	Manual testing	2⁶⁹	2⁷⁰		-	-	23.23	-	-
2022-01-20	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	46.46	-	-

ECM factoring results:

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	1.731

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-07-29	S00030	op9020-usff	50000	5000000						3	0.632
2014-07-23	Travis Glenn Russo	i5-spare	50000	5000000						3	0.632
2017-08-30	bayanne	iMac	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-09-13	ANONYMOUS	v4_computers	31F34D1CC444A37A	0.713
2000-11-15	ANONYMOUS	v4_computers	31F34D1CC444A37A	0.713

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 (P-1 stage 1)

B1 = 305000, B2 = 9683750 (P-1 stage 2)

B1 = 305000 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 65

TF double-checked to: 67.9

ECM T-Level=1.73 ~= -11-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