M3845119 Mersenne number exponent details

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M3845119

<<<

>>>

is 2 ^3845119 - 1

has 1157497 decimal digits

takes 0.404 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	-unknown-	-unknown-
PRP	09B393FD03DEC307	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	2⁶⁹	31.0489	68.1159%	15000000	750000000	8.3828	11.1439%	39.4317	71.6691%	3.5531%
PrimeNet	2⁶⁰	0.0399	63.3333%	17000	340000	0.0053	3.1943%	0.0452	64.5046%	1.1713%
GPU72	2⁶⁴	0.9257	65.6250%	24000	500000	0.0076	2.2278%	0.9333	66.3908%	0.7658%
Difference	+5	+30.1232	+2.4909%	+14976000	+749500000	+8.3752	+8.9161%	+38.4984	+5.2783%	+5.2783%

Known prime factors (1 factor, 75.8 bits, 0.00197119% 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
3845119	65536965626596264497239	23	75.795	8522098487276501 31 × 43 × 4789 × 1334970173	2021-10-27	4789	1334970173	2,111.1	11.077	20.688

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-27T16:22:00	Carsten Kossendey	leela	20000	270000		-		-	-	0.005	-	-	0.860%
2011-10-25T11:44:00	Squeeky_Squirrel	T7500_2200	70000	1137500		-		-	-	0.020	-	-	1.846%
2014-10-18T13:18:00	Jocelyn Larouche	Manual testing	86692	86692		-		-	-	0.013	-	-	0.708%
2016-02-03T10:08:10	Jocelyn Larouche	Manual testing	239500	2395000	6	-		-	-	0.054	-	-	2.780%
2020-11-23T01:55:57	Carlos Pinho	HomeComputer	173000	4675000	6	-		-	-	0.064	-	-	3.085%
2021-02-08T02:50:19	axn	Manual testing	15000000	750000000		-		-	-	8.383	-	-	11.144%
2022-03-03T00:13:25	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.725%
2022-03-22T11:10:06	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.773%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:41	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.040	-	-
2009-02-26T16:01:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.040	-	-
2011-03-05T11:07:00	markr	ut	2⁶¹	2⁶²		-	-	0.080	-	-
2012-02-20T20:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.415	-	-
2016-02-23T16:29:41	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.255	-	-
2015-01-18T21:00:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.511	-	-
2015-01-18T21:00:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.972	-	-
2016-02-28T22:17:22	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.943	-	-
2016-11-21T15:09:27	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.887	-	-
2018-08-13T14:25:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.774	-	-
2020-10-26T10:35:17	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	15.55	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.254 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	2.254 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.803
50000	5000000	65536965626596264497239	3	0.451

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-25T10:05:00	willreid	jing	50000	5000000						3	0.451
2012-09-04T20:27:00	oodaira	Linux01	50000	5000000						3	0.451
2016-01-25T20:49:30	Bruce	agent86	50000	5000000						3	0.451
2017-09-21T02:40:50	jafarism	jafarism-r07	50000	5000000						3	0.451
2021-10-27T12:44:46	daveward2005	Dave2	50000	5000000	65536965626596264497239	75.795	3	2	4505556057267057	3	0.451

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-07T00:00:00	Stephen Wood	v4_computers	E59C751B215355__	0.404

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-11-02T02:37:52

LaurV

Zero818

65536965626596264497239

09B393FD03DEC307

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 = 15000000, B2 = 750000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 173000, B2 = 4675000 (P-1 stage 2)

B1 = 239500, B2 = 2395000 (P-1 stage 2)

B1 = 239500 (P-1 stage 1)

B1 = 173000 (P-1 stage 1)

B1 = 70000, B2 = 1137500 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 86692 (P-1 stage 1)

B1 = 70000 (P-1 stage 1)

B1 = 20000, B2 = 270000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-22T11:10:06+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