M3745867 Mersenne number exponent details

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M3745867

<<<

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is 2 ^3745867 - 1

has 1127619 decimal digits

takes 0.393 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	DA51EF3D494582F1	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	7.9325	67.1642%	500000	130364850	1.1537	7.7719%	9.0861	69.7162%	2.5520%
PrimeNet	2⁶⁰	0.0410	63.3333%	16000	320000	0.0050	3.0902%	0.0460	64.4664%	1.1331%
GPU72	2⁶⁴	0.9502	65.6250%	22000	450000	0.0069	2.1103%	0.9571	66.3504%	0.7254%
Difference	+3	+6.9823	+1.5392%	+478000	+129914850	+1.1468	+5.6617%	+8.1290	+3.3658%	+3.3658%

Known prime factors (1 factor, 101.8 bits, 0.00271848% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3745867	4508530433055582323730988228297	31	101.831	601800655636676679088044 2² × 3 × 13933 × 1076587 × 1089709 × 3068083	2015-11-14	1089709	3068083	4.193e+10	0.1824	0.3377

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:44:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	1.150%
2013-03-14T05:30:00	Squeeky_Squirrel	T7500_2200	110000	2035000		-		-	-	0.033	-	-	2.956%
2015-11-14T16:16:38	mikr	MSI	1600000	66000000	12		4508530433055582323730988228297	31	101.831	0.778	0.787	1.556	7.948%
2022-05-17T01:12:23	Jocelyn Larouche	Manual testing	500000	130364850		-		-	-	1.154	-	-	7.772%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-05T16:15:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-06T21:14:00	markr	Manual testing	2¹	2⁶²		-	-	0.164	-	-
2012-05-10T01:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.426	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.524	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.997	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.897 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	0.897 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-11-04T20:32:00	willreid	jing	50000	5000000						3	0.448
2012-05-29T12:04:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.448

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-05T00:00:00	ANONYMOUS	v4_computers	DA51EF3D494582F1	0.393
1999-12-23T00:00:00	ANONYMOUS	v4_computers	DA51EF3D494582F1	0.393

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:17:52

kkmrkkblmbrbk

Manual testing

4508530433055582323730988228297

7433BA64195294__

2017-12-04T02:29:40

Oliver Kruse

Threadripper

4508530433055582323730988228297

7433BA64195294__

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 = 500000, B2 = 130364850 (P-1 stage 2)

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

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

B1 = 110000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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