M2543797 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	2⁶⁸	23.4315	67.6471%	3000000	135000000	1.0250	8.2627%	24.4565	70.3203%	2.6732%
PrimeNet	2⁵⁹	0.0302	62.7119%	11000	200000	0.0021	2.6841%	0.0323	63.7127%	1.0008%
GPU72	2⁶³	0.6274	65.0794%	12000	180000	0.0021	1.4773%	0.6295	65.5952%	0.5159%
Difference	+5	+22.8040	+2.5677%	+2988000	+134820000	+1.0229	+6.7854%	+23.8269	+4.7250%	+4.7250%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2543797	479912689957526239727	21	68.701	94329989766779 13 × 97 × 74805701639	2021-04-11	97	74805701639	41.434	409.90	765.58

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.236%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.755%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.265%
2011-01-03T01:03:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.366%
2011-01-08T14:34:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.531%
2011-03-04T20:21:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.072	-	-	3.959%
2018-08-13T10:35:02	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.048%
2018-09-22T12:03:03	mikr	MSI	3000000	135000000	12	-		-	-	1.025	-	-	8.263%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	Brap_On	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31T19:48:00	Sturle Sunde	aalto.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-15T14:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-11-09T15:28:00	lycorn	snail	2⁶²	2⁶³		-	-	0.386	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.772	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.469	-	-
2015-11-08T21:03:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.938	-	-
2017-08-08T13:42:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.875	-	-
2019-04-01T13:34:43	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.416 GHz-days
Estimated T-Level:	22.018

Digits	B1	Curves	Complete	FacMiss
20	11000	113 / 100	1.130	32.120%
25	50000	113 / 280	0.404	66.745%

New Calculation Method

Total ECM effort:	10.416 GHz-days
Estimated T-Level:	22.018

Digits	B1	Complete	FacMiss
20	11000	3.645	2.612%
25	50000	0.329	71.932%
30	250000	0.020	97.992%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		109	10.05
50000	5000000	479912689957526239727	4	0.369

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-12T21:09:00	Matthias Eckoldt	serverSP	50000	5000000						3	0.277
2010-07-02T21:18:00	Lupo	yorick	50000	5000000						3	0.277
2012-09-27T16:48:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.277
2014-04-02T02:24:00	Syntony	Geomancer	50000	5000000						3	0.277
2014-04-02T02:34:00	Syntony	Geomancer	50000	5000000						3	0.277
2014-04-02T02:38:00	Syntony	Geomancer	50000	5000000						3	0.277
2014-04-02T02:48:00	Syntony	Geomancer	50000	5000000						3	0.277
2014-04-02T02:58:00	Syntony	Geomancer	50000	5000000						3	0.277
2014-04-02T03:07:00	Syntony	Geomancer	50000	5000000						3	0.277
2018-02-21T13:15:02	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2018-11-19T18:49:19	Daniel Koszta	_	50000	5000000						3	0.277
2020-06-04T05:31:31	GAN	KL-10	50000	5000000						3	0.277
2020-06-22T23:58:57	LaurV	3tits	50000	5000000						3	0.277
2020-07-01T20:38:02	IanGlencross	glenx24	50000	5000000						3	0.277
2020-07-08T21:26:08	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2020-07-14T12:17:19	GAN	LMS-15	50000	5000000						3	0.277
2020-07-20T16:05:48	GAN	LMS-11	50000	5000000						3	0.277
2020-07-27T01:48:47	GAN	OSB-02	50000	5000000						3	0.277
2020-08-03T10:36:16	GAN	LMS-13	50000	5000000						3	0.277
2020-08-11T05:55:42	GAN	LMS-02	50000	5000000						3	0.277
2020-08-29T06:44:46	mnd9	libproj	50000	5000000						7	0.645
2020-10-03T15:49:33	LaurV	3tits	50000	5000000						7	0.645
2020-10-26T15:55:45	mnd9	75204	50000	5000000						7	0.645
2020-12-01T18:53:15	lycorn	colab_S_1	50000	5000000						7	0.645
2021-02-03T15:00:27	Zenzoma	AMD3970X	50000	5000000						7	0.645
2021-03-04T04:46:02	Zenzoma	AM3700X_1	50000	5000000						7	0.645
2021-03-07T19:49:19	mnd9	75204b	50000	5000000						7	0.645
2021-04-11T01:34:41	mnd9	50869	50000	5000000	479912689957526239727	68.701	4	2	4919440889838926	4	0.369

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	5DF2B0AC762CD4A9	0.176
2018-06-10T20:07:34	kkmrkkblmbrbk	old	5DF2B0AC762CD4A9	0.176

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 = 135000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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