M3745891 Mersenne number exponent details

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M3745891

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is 2 ^3745891 - 1

has 1127626 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	F4AE37F1DCA9F842	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	7.9324	67.1642%	1600000	66000000	0.7780	7.9478%	8.7104	69.7739%	2.6097%
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	+6.9822	+1.5392%	+1578000	+65550000	+0.7711	+5.8375%	+7.7533	+3.4235%	+3.4235%

Known prime factors (1 factor, 66.1 bits, 0.00176507% 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
3745891	80049409619731455551	20	66.118	10684962485525 5² × 193 × 617 × 3589141	2015-11-15	617	3589141	6.9522	0.0299	0.0556

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%
2013-03-14T06:56:00	Squeeky_Squirrel	T7500_2200	110000	2035000		-		-	-	0.033	-	-	2.956%
2015-11-15T01:56:17	mikr	MSI	1600000	66000000	12		80049409619731455551	20	66.118	0.778	0.787	1.556	7.948%
2022-05-26T12:47:37	Jocelyn Larouche	Manual testing	200000	130364850		-	skipped known factor: 80049409619731455551	-	-	1.110	-	-	6.810%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1999-08-16T00:00:00	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	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

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
2009-09-05T12:34:00	willreid	jing	50000	5000000						3	0.448
2012-05-28T17:18:00	S00030	op9020-usff	50000	5000000						3	0.448

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-21T00:00:00	Joel Armengaud	v4_computers	F4AE37F1DCA9F842	0.393
1999-08-31T00:00:00	ANONYMOUS	v4_computers	F4AE37F1DCA9F842	0.393

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:17:52

kkmrkkblmbrbk

Manual testing

80049409619731455551

FCC31FF84C5A7B__

2017-12-04T04:17:24

Oliver Kruse

GTX-0

80049409619731455551

FCC31FF84C5A7B__

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 = 200000, B2 = 130364850 (P-1 stage 2)

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

B1 = 1600000 (P-1 stage 1)

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

B1 = 200000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-26T12:47:37+00:00

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