M870047 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	34.1521	70.1493%	131072	13107200	0.0295	3.6336%	34.1816	71.2339%	1.0846%
PrimeNet	2⁴⁰	0.0000	50.0000%	8000	340000	0.0009	23.0677%	0.0009	61.5338%	11.5338%
GPU72	2⁴⁴	0.0000	54.5455%	14000	550000	0.0015	17.6138%	0.0015	62.5517%	8.0063%
Difference	+23	+34.1521	+15.6038%	+117072	+12557200	+0.0279	-13.9802%	+34.1800	+8.6822%	+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
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.208%
2002-02-17T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.444%
2002-04-14T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.799%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.295%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.938%
2002-12-16T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.015	-	-	2.722%
2003-08-25T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.634%
2011-02-21T01:22:00	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.007	-	-	1.150%
2011-07-12T13:44:00	Jocelyn Larouche	Manual testing	238764	238764		-		-	-	0.008	-	-	1.259%
2011-08-31T00:06:00	Jocelyn Larouche	Manual testing	397941	397941		-		-	-	0.014	-	-	1.610%
2012-01-22T03:55:00	Jocelyn Larouche	Manual testing	795882	795882		-		-	-	0.028	-	-	2.169%
2012-03-29T23:13:00	Jocelyn Larouche	Manual testing	1193823	1193823		-		-	-	0.042	-	-	2.540%
2012-09-21T00:58:00	Jocelyn Larouche	Manual testing	1740094	1740094		-		-	-	0.061	-	-	2.914%
2014-12-18T00:08:00	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
2000-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.011	-	-
2001-12-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.022	-	-
2003-09-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.044	-	-
2022-03-07T09:34:19	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.044	-	-
2004-06-04T00:00:00	Sturle Sunde	v4_computers	2¹	2⁶⁰		-	-	0.177	-	-
2010-06-03T02:30:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.177	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.019 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	14.019 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

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
2007-09-06T08:27:00	Chad Davis	Bayes	50000	5000000						1	0.028
2008-01-26T19:58:00	Sturle Sunde	minister	50000	5000000						3	0.084
2008-10-20T20:52:00	Sturle Sunde	v23	50000	5000000						3	0.084
2009-02-07T00:28:00	Sturle Sunde	v23	50000	5000000						3	0.084
2009-05-08T04:38:00	maxybo	CB418E216	50000	5000000						3	0.084
2009-09-02T10:55:00	Lackó	Iroda_Eva	50000	5000000						3	0.084
2009-10-18T20:44:00	JimBa	atlserv	50000	5000000						3	0.084
2010-01-29T16:15:00	Lupo	yorick	50000	5000000						3	0.084
2010-06-17T12:07:00	Charles A. Morris	pulsar	50000	5000000						3	0.084
2010-12-31T04:39:00	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.084
2011-04-08T13:45:00	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.084
2011-11-28T07:43:00	Pool Party	sts	50000	5000000						3	0.084
2012-08-14T06:21:00	soldake		50000	5000000						3	0.084
2012-09-23T19:07:00	Justin	temp1	50000	5000000						3	0.084
2013-02-06T08:10:00	gucs	echo3	50000	5000000						3	0.084
2013-04-22T03:09:00	gucs	echo3	50000	5000000						3	0.084
2013-07-05T16:49:00	gucs	echo3	50000	5000000						3	0.084
2013-09-21T06:42:00	gucs	echo3	50000	5000000						3	0.084
2013-12-08T10:47:00	gucs	echo3	50000	5000000						3	0.084
2014-02-05T19:19:00	gucs	echo3	50000	5000000						3	0.084
2014-03-21T11:54:00	gucs	echo3	50000	5000000						3	0.084
2014-04-20T23:16:00	gucs	echo3	50000	5000000						3	0.084
2014-06-04T23:41:00	Ryan Schulz	wenn	50000	5000000						15	0.420
2016-01-15T14:51:02	TJAOI	Manual testing	50000	5000000						21	0.588
2016-10-28T16:21:09	TJAOI	Manual testing	50000	5000000						90	2.518
2017-03-17T17:35:52	TJAOI	Manual testing	50000	5000000						91	2.546
2019-11-18T17:48:50	TJAOI	Manual testing	250000	25000000						44	6.156

date	userid	compid	res64	spent (GHz-days)
2002-01-28T00:00:00	ANONYMOUS	v4_computers	0213372E95893EE8	0.021

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

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10⁷

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10³

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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