M2478937 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	24.0445	67.6471%	2382500	85770100	0.6965	7.5475%	24.7411	70.0889%	2.4418%
PrimeNet	2⁵⁹	0.0310	62.7119%	10000	180000	0.0019	2.5339%	0.0329	63.6567%	0.9448%
GPU72	2⁶³	0.6438	65.0794%	11000	160000	0.0019	1.3797%	0.6458	65.5612%	0.4818%
Difference	+5	+23.4007	+2.5677%	+2371500	+85610100	+0.6946	+6.1678%	+24.0953	+4.5277%	+4.5277%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2478937	177508175218345998539207	24	77.232	35803284879435419 23 × 13597 × 114485883649	2020-12-13	13597	114485883649	19,240	627.33	1,171.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.234%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.785%
2010-11-20T12:24:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.263%
2011-01-20T11:04:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.378%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	120892	120892		-		-	-	0.012	-	-	0.917%
2014-10-27T05:20:00	mikr	MSI	2382500	85770100		-		-	-	0.697	-	-	7.547%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:15	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-15T06:26:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-09T00:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-08-21T03:34:00	David Campeau	Manual testing	2⁶²	2⁶³		-	-	0.396	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.792	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.507	-	-
2015-10-29T11:36:21	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.014	-	-
2017-07-22T20:28:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.029	-	-
2019-05-27T13:36:57	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.06	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.356 GHz-days
Estimated T-Level:	4.550

Digits	B1	Curves	Complete	FacMiss
20	11000	91 / 100	0.910	40.068%
25	50000	91 / 280	0.325	72.211%

New Calculation Method

Total ECM effort:	8.356 GHz-days
Estimated T-Level:	4.550

Digits	B1	Complete	FacMiss
20	11000	3.500	3.020%
25	50000	0.324	72.336%
30	250000	0.020	97.978%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		90	8.264
50000	5000000	177508175218345998539207	1	0.092

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-19T10:57:00	Wolfgang Fluck		50000	5000000						3	0.275
2010-03-23T06:29:00	James Classen	towerofart	50000	5000000						3	0.275
2012-06-06T15:53:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.275
2014-02-04T14:50:00	Falconiform	Falconiform	50000	5000000						3	0.275
2015-07-18T17:58:00	guru	w6	50000	5000000						3	0.275
2016-02-25T15:59:43	Jason U	Server7	50000	5000000						3	0.275
2016-06-23T09:21:12	Bruce	test	50000	5000000						3	0.275
2017-02-26T03:02:10	Bruce	eleven	50000	5000000						3	0.275
2017-08-06T16:32:35	S36049	Wolle5	50000	5000000						3	0.275
2017-12-20T23:27:48	Sebastian Hornbostel	V2	50000	5000000						3	0.275
2018-07-22T18:21:06	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.275
2019-09-30T08:55:25	storm5510	3570_Ivy_Bridge	50000	5000000						3	0.275
2020-05-10T11:29:13	daveward2005	Davy	50000	5000000						3	0.275
2020-05-24T06:59:01	Summy	CHB	50000	5000000						3	0.275
2020-06-15T00:52:04	mnd9	office2	50000	5000000						3	0.275
2020-06-28T10:37:09	mnd9	75203b	50000	5000000						3	0.275
2020-07-05T01:20:14	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.275
2020-07-11T08:36:11	MarkS	desktop-i7	50000	5000000						3	0.275
2020-07-17T12:54:39	mnd9	kitchen	50000	5000000						3	0.275
2020-07-23T07:51:21	GAN	LMS-11	50000	5000000						3	0.275
2020-07-30T05:41:23	GAN	LMS-12	50000	5000000						3	0.275
2020-08-06T17:50:29	GAN	LMS-14	50000	5000000						3	0.275
2020-08-15T02:15:14	GAN	LMS-18	50000	5000000						3	0.275
2020-09-09T06:01:25	J.R. Allen	lapacer	50000	5000000						7	0.643
2020-10-10T09:09:55	MarkS	desktop-i7	50000	5000000						7	0.643
2020-11-07T12:09:13	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.643
2020-12-13T11:57:12	Zenzoma	AMD3970X	50000	5000000	177508175218345998539207	77.232	1	2	6880640393632798	1	0.092

date	userid	compid	res64	spent (GHz-days)
1999-08-16T00:00:00	ANONYMOUS	v4_computers	402326B232982DF9	0.172
1999-09-30T00:00:00	ANONYMOUS	v4_computers	402326B232982DF9	0.172
2018-05-30T03:45:20	kkmrkkblmbrbk	old	402326B232982DF9	0.172

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 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 120892 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (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)

10²

10³

10⁴

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10⁷

10²

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10⁹

10¹⁰

10¹¹

10¹²

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