M2762671 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	21.5751	67.6471%	5000000	100000000	1.1396	8.2325%	22.7147	70.3105%	2.6635%
PrimeNet	2⁵⁹	0.0278	62.7119%	12000	220000	0.0026	2.8549%	0.0304	63.7764%	1.0645%
GPU72	2⁶³	0.5777	65.0794%	15000	240000	0.0031	1.7454%	0.5808	65.6889%	0.6095%
Difference	+5	+20.9974	+2.5677%	+4985000	+99760000	+1.1366	+6.4871%	+22.1339	+4.6217%	+4.6217%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2762671	24098277280067020204583	23	74.351	4361409172512221 17 × 33029 × 7767521897	2021-03-30	33029	7767521897	1,702.9	47.398	88.520

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.242%
2010-12-03T01:44:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.605%
2016-08-09T03:03:37	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	3.185%
2016-10-27T01:50:41	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	1.129%
2016-12-24T02:28:24	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.241%
2017-01-20T02:11:50	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.680%
2017-02-25T21:08:00	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	3.202%
2021-04-01T00:41:37	riccardo uberti	Colab_noGPU14	5000000	100000000	12	-		-	-	1.140	-	-	8.232%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.056	-	-
2009-01-31T04:48:00	Sturle Sunde	gorro.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-16T23:03:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.355	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.711	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.352	-	-
2016-02-08T11:13:49	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.705	-	-
2017-10-09T09:26:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.410	-	-
2019-02-21T01:08:08	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.82	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.036 GHz-days
Estimated T-Level:	4.250

Digits	B1	Curves	Complete	FacMiss
20	11000	85 / 100	0.850	42.559%
25	50000	85 / 280	0.304	73.778%

New Calculation Method

Total ECM effort:	9.036 GHz-days
Estimated T-Level:	4.250

Digits	B1	Complete	FacMiss
20	11000	2.773	6.247%
25	50000	0.251	77.806%
30	250000	0.015	98.465%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		67	6.965
50000	5000000	24098277280067020204583	4	0.416
50000	6534469		7	0.824
50000	6650000		7	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-15T10:44:00	willreid	jing	50000	5000000						3	0.312
2010-09-17T02:14:00	Kamil_Górski	thefault	50000	5000000						3	0.312
2013-03-03T22:58:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.312
2015-03-12T04:28:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-14T10:17:41	Sintax	cloud2	50000	5000000						3	0.312
2016-05-17T02:08:19	Jason U	Server7	50000	5000000						3	0.312
2017-01-15T06:22:08	Bruce	eleven	50000	5000000						3	0.312
2017-07-29T04:42:07	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.312
2017-12-28T12:58:20	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2018-10-04T06:12:52	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-05T05:37:18	GAN	LMS-03	50000	5000000						3	0.312
2020-08-13T13:40:27	daveward2005	Dave2	50000	5000000						3	0.312
2020-09-03T08:10:37	J.R. Allen	lapacer	50000	5000000						7	0.728
2020-10-07T15:35:20	LaurV	3tits	50000	5000000						7	0.728
2020-11-02T07:38:36	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.728
2020-12-07T07:34:55	George Woltman	x64-debug	50000	6534469						7	0.824
2021-01-15T17:26:44	Sergey Nosov	TS140-02	50000	5000000						7	0.728
2021-02-13T17:34:19	lycorn	colab_A_1	50000	6650000						7	0.831
2021-03-18T13:34:32	Lisander Viaene	Asus_TUF_Gaming	50000	5000000						3	0.312
2021-03-30T15:25:18	daveward2005	MW	50000	5000000	24098277280067020204583	74.351	4	2		4	0.416

date	userid	compid	res64	spent (GHz-days)
1999-09-30T00:00:00	ANONYMOUS	v4_computers	714004873F6AB7C3	0.213
2018-08-18T10:55:41	kkmrkkblmbrbk	old	714004873F6AB7C3	0.213

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 = 5000000, B2 = 100000000 (P-1 stage 2)

B1 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2700000 (P-1 stage 1)

B1 = 294451, B2 = 2944510 (P-1 stage 2)

B1 = 142000, B2 = 4730000 (P-1 stage 2)

B1 = 294451 (P-1 stage 1)

B1 = 110000, B2 = 2365000 (P-1 stage 2)

B1 = 204480 (P-1 stage 1)

B1 = 170400 (P-1 stage 1)

B1 = 142000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 2048 (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