M3764477 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

152EDA1CA59B391D

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	63.4751	68.5714%	1600000	66000000	0.7780	6.1512%	64.2531	70.5047%	1.9332%
PrimeNet	2⁶⁰	0.0408	63.3333%	17000	340000	0.0053	3.1828%	0.0461	64.5003%	1.1670%
GPU72	2⁶⁴	0.9455	65.6250%	24000	450000	0.0072	2.1596%	0.9527	66.3674%	0.7424%
Difference	+6	+62.5296	+2.9464%	+1576000	+65550000	+0.7708	+3.9916%	+63.3004	+4.1373%	+4.1373%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

63.4751

68.5714%

1600000

66000000

0.7780

6.1512%

64.2531

70.5047%

1.9332%

PrimeNet

2⁶⁰

0.0408

63.3333%

17000

340000

0.0053

3.1828%

0.0461

64.5003%

1.1670%

GPU72

2⁶⁴

0.9455

65.6250%

24000

450000

0.0072

2.1596%

0.9527

66.3674%

0.7424%

Difference

+62.5296

+2.9464%

+1576000

+65550000

+0.7708

+3.9916%

+63.3004

+4.1373%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3764477	18724698810290532267511	23	73.987	2487025264105815 3 × 5 × 19 × 8726404435459	2021-11-01	19	8726404435459	945.36	72,405	135,232

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3764477

18724698810290532267511

73.987

2487025264105815
3 × 5 × 19 × 8726404435459

2021-11-01

8726404435459

945.36

72,405

135,232

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-12T06:21:00	Carsten Kossendey	durandal	20000	265000		-		-	-	0.005	-	-	0.731%
2012-04-05T22:08:00	Squeeky_Squirrel	P4_2600	110000	2035000		-		-	-	0.033	-	-	2.077%
2016-01-18T01:35:52	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.151%
2022-03-03T20:37:56	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.624%
2022-03-22T11:10:18	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.667%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:38	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-02T16:30:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-22T16:26:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.082	-	-
2012-03-23T23:44:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.424	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.261	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.522	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.993	-	-
2016-02-28T22:17:33	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.985	-	-
2016-11-09T06:37:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.970	-	-
2019-01-21T12:54:00	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.940	-	-
2019-02-08T06:02:17	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	7.940	-	-
2020-12-06T06:00:29	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	15.88	-	-
2021-03-28T17:26:50	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	31.76	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.440 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	3.440 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.742	47.619%
25	50000	0.067	93.514%
30	250000	0.004	99.588%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.842
50000	5000000	18724698810290532267511	4	0.598

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-14T21:35:00	Sid & Andy	Slinky	50000	5000000						3	0.449
2012-07-15T15:53:00	S36049	Wolle5	50000	5000000						3	0.449
2015-12-18T22:00:13	FreeTibet	DR	50000	5000000						3	0.449
2017-07-22T19:28:17	Bruce	Desk10	50000	5000000						3	0.449
2021-08-21T05:10:20	MarkS	laptop64	50000	5000000						7	1.047
2021-11-01T18:15:58	daveward2005	Dave2	50000	5000000	18724698810290532267511	73.987	4	2	1545687858733850	4	0.598

date	userid	compid	res64	spent (GHz-days)
1999-08-16T00:00:00	ANONYMOUS	v4_computers	9392A86F01F60E__	0.395

date

userid

compid

res64

spent (GHz-days)

1999-08-16T00:00:00

ANONYMOUS

v4_computers

9392A86F01F60E__

0.395

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 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 110000, B2 = 2035000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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