M2616577 Mersenne number exponent details

Residue

Status

L-L

AC19F45CC29F48A3

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	11.3560	67.1642%	400000	4000000	0.0668	3.9308%	11.4228	68.4549%	1.2907%
PrimeNet	2⁵⁹	0.0293	62.7119%	11000	200000	0.0024	2.6980%	0.0317	63.7179%	1.0060%
GPU72	2⁶³	0.6100	65.0794%	12000	200000	0.0025	1.5323%	0.6125	65.6144%	0.5351%
Difference	+4	+10.7461	+2.0848%	+388000	+3800000	+0.0643	+2.3985%	+10.8103	+2.8404%	+2.8404%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.3560

67.1642%

400000

4000000

0.0668

3.9308%

11.4228

68.4549%

1.2907%

PrimeNet

2⁵⁹

0.0293

62.7119%

11000

200000

0.0024

2.6980%

0.0317

63.7179%

1.0060%

GPU72

2⁶³

0.6100

65.0794%

12000

200000

0.0025

1.5323%

0.6125

65.6144%

0.5351%

Difference

+10.7461

+2.0848%

+388000

+3800000

+0.0643

+2.3985%

+10.8103

+2.8404%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2616577	25604795568195777760439	23	74.439	4892803760064347 104021 × 47036692207	2019-03-01	104021	47036692207	1,989.8	287.01	536.04

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2616577

25604795568195777760439

74.439

4892803760064347
104021 × 47036692207

2019-03-01

104021

47036692207

1,989.8

287.01

536.04

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.295%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.914%
2010-11-17T22:11:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.317%
2010-12-13T03:19:00	markr	tiny	100000	2125000		-		-	-	0.024	-	-	2.783%
2014-10-12T23:56:00	Jocelyn Larouche	Manual testing	124530	124530		-		-	-	0.014	-	-	1.081%
2016-05-24T01:15:56	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.043	-	-	3.518%
2017-07-20T22:03:19	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.931%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-31T20:31:00	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-22T06:05:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.117	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.375	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.750	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.428	-	-
2016-01-17T23:07:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.856	-	-
2017-08-30T11:24:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.712	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.402 GHz-days
Estimated T-Level:	1.650

Digits	B1	Curves	Complete	FacMiss
20	11000	33 / 100	0.330	71.773%
25	50000	33 / 280	0.118	88.864%

New Calculation Method

Total ECM effort:	3.402 GHz-days
Estimated T-Level:	1.650

Digits	B1	Complete	FacMiss
20	11000	1.065	34.489%
25	50000	0.096	90.827%
30	250000	0.006	99.409%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	3.092
50000	5000000	25604795568195777760439	3	0.309

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-27T16:19:00	paulie	iMac3.4	50000	5000000						3	0.309
2010-06-12T02:38:00	SubPrime	abd0	50000	5000000						3	0.309
2012-11-21T23:29:00	Brian V.	dxl5420	50000	5000000						3	0.309
2014-09-10T00:24:00	Syntony	Geomancer	50000	5000000						3	0.309
2015-11-18T17:06:25	Syntony	Hadfield	50000	5000000						3	0.309
2016-03-27T14:57:20	Jason U	Server7	50000	5000000						3	0.309
2016-08-20T13:04:40	ANONYMOUS	PD925	50000	5000000						3	0.309
2016-08-20T13:25:30	ANONYMOUS	PD925	50000	5000000						3	0.309
2017-10-26T05:05:39	Sebastian Hornbostel	V2	50000	5000000						3	0.309
2018-04-22T00:30:04	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2019-03-01T06:37:24	Chang Chia-Tche	ex-ctcpc	50000	5000000	25604795568195777760439	74.439	3	2		3	0.309

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	AC19F45CC29F48A3	0.202
2018-07-07T00:01:31	kkmrkkblmbrbk	old	AC19F45CC29F48A3	0.202

date

userid

compid

res64

spent (GHz-days)

1999-04-13T00:00:00

ANONYMOUS

v4_computers

AC19F45CC29F48A3

0.202

2018-07-07T00:01:31

kkmrkkblmbrbk

old

AC19F45CC29F48A3

0.202

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 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 124530 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (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

10⁵

10⁶

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