M3773359 Mersenne number exponent details

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M3773359

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is 2 ^3773359 - 1

has 1135895 decimal digits

takes 0.396 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	8BF46C22BA6C9677	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	7.8747	67.1642%	500000	130364850	1.1537	7.7782%	9.0283	69.7182%	2.5540%
PrimeNet	2⁶⁰	0.0407	63.3333%	17000	340000	0.0053	3.1840%	0.0460	64.5008%	1.1675%
GPU72	2⁶⁴	0.9433	65.6250%	24000	450000	0.0072	2.1605%	0.9505	66.3677%	0.7427%
Difference	+3	+6.9314	+1.5392%	+476000	+129914850	+1.1465	+5.6176%	+8.0779	+3.3505%	+3.3505%

Known prime factors (1 factor, 104.8 bits, 0.00277729% 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
3773359	35239870623661517173526232840511	32	104.797	4669562400988286189244945 3 × 5 × 11 × 17 × 59 × 523 × 19421 × 72973 × 38067629	2016-02-21	72973	38067629	3.463e+10	0.3264	0.5899

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-13T10:15:00	Carsten Kossendey	durandal	20000	265000		-		-	-	0.005	-	-	1.151%
2012-04-10T14:17:00	Squeeky_Squirrel	P4_2600	110000	2035000		-		-	-	0.033	-	-	2.960%
2016-02-21T04:31:40	mikr	MSI	1600000	66000000	12		35239870623661517173526232840511	32	104.797	0.778	0.793	1.556	7.954%
2022-05-17T01:12:22	Jocelyn Larouche	Manual testing	500000	130364850		-	skipped known factor: 35239870623661517173526232840511	-	-	1.154	-	-	7.778%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1998-07-29T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1998-08-09T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1998-08-30T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1998-09-13T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1998-10-11T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
1998-10-29T00:00:00	quantumfoam5678	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-02T07:23:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-16T08:24:00	markr	Manual testing	2¹	2⁶²		-	-	0.163	-	-
2012-03-23T23:45:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.423	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.260	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.520	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.990	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.347 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.347 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.347

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-16T01:06:00	Lupo	corpse	50000	5000000						3	0.449
2012-07-26T21:09:00	Lukasz Wrobel	back	50000	5000000						3	0.449
2015-12-24T05:45:55	sannerud.com	Jens2010	50000	5000000						3	0.449

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-29T00:00:00	quantumfoam5678	v4_computers	8BF46C22BA6C9677	0.396
1998-08-09T00:00:00	quantumfoam5678	v4_computers	8BF46C22BA6C9677	0.396
1998-08-30T00:00:00	quantumfoam5678	v4_computers	8BF46C22BA6C9677	0.396
1998-09-13T00:00:00	quantumfoam5678	v4_computers	8BF46C22BA6C9677	0.396
1998-10-11T00:00:00	quantumfoam5678	v4_computers	8BF46C22BA6C9677	0.396
1998-10-29T00:00:00	quantumfoam5678	v4_computers	8BF46C22BA6C9677	0.396
2000-01-19T00:00:00	ANONYMOUS	v4_computers	8BF46C22BA6C9677	0.396

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:28:46

kkmrkkblmbrbk

Manual testing

35239870623661517173526232840511

EB2C8EC6DD2A5F__

2017-12-07T14:17:14

Oliver Kruse

Threadripper

35239870623661517173526232840511

EB2C8EC6DD2A5F__

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