M870 047 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	34.1521	70.1493%	131072	13107200	0.0295	3.6336%	34.1816	71.2339%
Target	2⁴⁴	0.0000	54.5455%	14000	550000	0.0015	17.6138%	0.0015	62.5517%
Difference	+23	+34.1521	+15.6038%	+117072	+12557200	+0.0279	-13.9802%	+34.1800	+8.6822%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
870047	423062685589476116927251684471	30	98.417	243126340065235623436005 3 × 5 × 29 × 94819 × 5325217 × 1106904301	2014-12-18	5325217	1106904301	1.406e+11	2.2976	3.9606

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.208%
2002-02-17	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.444%
2002-04-14	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.799%
2002-05-25	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.295%
2002-06-29	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.938%
2002-12-16	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.015	-	-	2.722%
2003-08-25	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.634%
2011-02-21	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.007	-	-	1.150%
2011-07-12	Jocelyn Larouche	Manual testing	238764	238764		-		-	-	0.008	-	-	1.259%
2011-08-31	Jocelyn Larouche	Manual testing	397941	397941		-		-	-	0.014	-	-	1.610%
2012-01-22	Jocelyn Larouche	Manual testing	795882	795882		-		-	-	0.028	-	-	2.169%
2012-03-29	Jocelyn Larouche	Manual testing	1193823	1193823		-		-	-	0.042	-	-	2.540%
2012-09-21	Jocelyn Larouche	Manual testing	1740094	1740094		-		-	-	0.061	-	-	2.914%
2014-12-18	mikr	Dell	131072	13107200			423062685589476116927251684471	30	98.417	0.029	0.042	0.059	3.634%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-24	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2000-12-31	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.011	-	-
2001-12-08	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.022	-	-
2003-09-09	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.044	-	-
2022-03-07	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.044	-	-
2004-06-04	Sturle Sunde	v4_computers	2¹	2⁶⁰		-	-	0.177	-	-
2010-06-03	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.177	-	-

ECM factoring results:

Total ECM effort:	14.019 GHz-days
Estimated T-Level:	25.658

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	7.863
250000	25000000		44	6.156

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-06	Chad Davis	Bayes	50000	5000000						1	0.028
2008-01-26	Sturle Sunde	minister	50000	5000000						3	0.084
2008-10-20	Sturle Sunde	v23	50000	5000000						3	0.084
2009-02-07	Sturle Sunde	v23	50000	5000000						3	0.084
2009-05-08	maxybo	CB418E216	50000	5000000						3	0.084
2009-09-02	Lackó	Iroda_Eva	50000	5000000						3	0.084
2009-10-18	JimBa	atlserv	50000	5000000						3	0.084
2010-01-29	Lupo	yorick	50000	5000000						3	0.084
2010-06-17	Charles A. Morris	pulsar	50000	5000000						3	0.084
2010-12-31	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.084
2011-04-08	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.084
2011-11-28	Pool Party	sts	50000	5000000						3	0.084
2012-08-14	soldake		50000	5000000						3	0.084
2012-09-23	Justin	temp1	50000	5000000						3	0.084
2013-02-06	gucs	echo3	50000	5000000						3	0.084
2013-04-22	gucs	echo3	50000	5000000						3	0.084
2013-07-05	gucs	echo3	50000	5000000						3	0.084
2013-09-21	gucs	echo3	50000	5000000						3	0.084
2013-12-08	gucs	echo3	50000	5000000						3	0.084
2014-02-05	gucs	echo3	50000	5000000						3	0.084
2014-03-21	gucs	echo3	50000	5000000						3	0.084
2014-04-20	gucs	echo3	50000	5000000						3	0.084
2014-06-04	Ryan Schulz	wenn	50000	5000000						15	0.420
2016-01-15	TJAOI	Manual testing	50000	5000000						21	0.588
2016-10-28	TJAOI	Manual testing	50000	5000000						90	2.518
2017-03-17	TJAOI	Manual testing	50000	5000000						91	2.546
2019-11-18	TJAOI	Manual testing	250000	25000000						44	6.156

date	userid	compid	res64	spent (GHz-days)
1997-01-01	James Reimer		0213372E95893EE8	0.021
2002-01-28	ANONYMOUS	v4_computers	0213372E95893EE8	0.021

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28

Oliver Kruse

GTX-3

423062685589476116927251684471

89034804AE653C__

2017-10-14

Oliver Kruse

Threadripper

89034804AE653C__

2017-12-19

ATH

ec2-1xf

423062685589476116927251684471

89034804AE653C__

2020-04-22

Oliver Kruse

AddPrpType5

423062685589476116927251684471

3A8DA2A28E009C__

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 = 1740094 (P-1 stage 1)

B1 = 1193823 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 795882 (P-1 stage 1)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 397941 (P-1 stage 1)

B1 = 238764 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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