M3747847 Mersenne number exponent details

≡

M3747847

<<<

>>>

is 2 ^3747847 - 1

has 1128215 decimal digits

takes 0.394 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	B4B92A758EF351BB	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	2⁷⁰	63.7568	68.5714%	1600000	66000000	0.7780	6.1482%	64.5348	70.5037%	1.9323%
PrimeNet	2⁶⁰	0.0410	63.3333%	16000	320000	0.0050	3.0905%	0.0459	64.4665%	1.1332%
GPU72	2⁶⁴	0.9497	65.6250%	22000	450000	0.0069	2.1105%	0.9566	66.3505%	0.7255%
Difference	+6	+62.8071	+2.9464%	+1578000	+65550000	+0.7711	+4.0378%	+63.5782	+4.1533%	+4.1533%

Known prime factors (1 factor, 71.4 bits, 0.00190641% 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
3747847	3223925886224142478529	22	71.449	430103721713312 2⁵ × 13440741303541	2021-08-13	32	13440741303541	241.14	111,520	208,289

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:45:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.730%
2013-03-15T01:17:00	Squeeky_Squirrel	T7500_2200	110000	2035000		-		-	-	0.033	-	-	2.076%
2015-11-22T02:04:08	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.148%
2022-03-03T20:39:05	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.624%
2022-03-22T11:09:13	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.666%
2022-05-25T14:13:59	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.379%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-05T06:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-04T20:59:00	markr	Manual testing	2¹	2⁶²		-	-	0.164	-	-
2012-05-10T01:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.426	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.262	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.524	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.997	-	-
2016-02-26T10:03:31	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.994	-	-
2016-11-06T04:15:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.988	-	-
2018-06-18T10:07:26	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.976	-	-
2020-12-09T13:21:03	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	15.95	-	-
2021-03-21T08:32:38	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	31.90	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.014 GHz-days
Estimated T-Level:	0.950

Digits	B1	Curves	Complete	FacMiss
20	11000	19 / 100	0.190	82.617%
25	50000	19 / 280	0.068	93.428%

New Calculation Method

Total ECM effort:	3.014 GHz-days
Estimated T-Level:	0.950

Digits	B1	Complete	FacMiss
20	11000	0.753	47.085%
25	50000	0.070	93.264%
30	250000	0.004	99.560%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.793
50000	6800000	3223925886224142478529	7	1.220

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-03T01:19:00	freeshow	Ra	50000	5000000						3	0.448
2012-05-31T15:11:00	Smurgs	Praca	50000	5000000						3	0.448
2015-12-04T21:11:51	Bruce	agent86	50000	5000000						3	0.448
2017-07-08T14:38:39	Bruce	Desk10	50000	5000000						3	0.448
2021-08-13T03:37:27	kutens	pve1	50000	6800000	3223925886224142478529	71.449	7	2	6576421677581387	7	1.220

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-05T00:00:00	ANONYMOUS	v4_computers	B4B92A758EF351BB	0.394
1999-11-04T00:00:00	ANONYMOUS	v4_computers	B4B92A758EF351BB	0.394

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-15T10:58:43

GURA LOVE

3223925886224142478529

96A380D5D118AA65

2021-08-16T07:16:30

kutens

ryzen2

3223925886224142478529

96A380D5D118AA65

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 = 100000, 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 = 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

10¹⁴

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-25T14:13:59+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