M3109697 Mersenne number exponent details

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M3109697

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is 2 ^3109697 - 1

has 936113 decimal digits

takes 0.265 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	7C7DB15DF1B12109	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	2⁶⁹	38.3918	68.1159%	3109697	668289930	4.8563	9.7010%	43.2481	71.2090%	3.0931%
PrimeNet	2⁶⁰	0.0494	63.3333%	13000	240000	0.0031	2.6437%	0.0525	64.3027%	0.9693%
GPU72	2⁶⁴	1.1446	65.6250%	14000	240000	0.0032	1.5080%	1.1478	66.1434%	0.5184%
Difference	+5	+37.2472	+2.4909%	+3095697	+668049930	+4.8530	+8.1930%	+42.1002	+5.0656%	+5.0656%

Known prime factors (1 factor, 95.1 bits, 0.00305881% 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
3109697	43038535740662936130082961071	29	95.120	6920052940955812757655 3 × 5 × 269 × 3067 × 6841 × 106129 × 770191	2018-08-29	106129	770191	3.192e+9	0.0176	0.0267

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.202%
2009-07-03T21:39:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.651%
2011-08-23T11:53:00	Squeeky_Squirrel	T7500_2200	100000	2125000		-		-	-	0.026	-	-	2.253%
2016-08-31T03:20:26	Jocelyn Larouche	low4M	100000	4250000	6	-		-	-	0.040	-	-	2.635%
2016-12-28T01:45:58	Jocelyn Larouche	low 4M	120000	120000		-		-	-	0.015	-	-	0.827%
2017-01-30T01:30:33	Jocelyn Larouche	low 4M	156000	156000		-		-	-	0.019	-	-	0.960%
2017-02-04T18:42:37	Jocelyn Larouche	low 4M	187200	187200		-		-	-	0.023	-	-	1.060%
2017-02-16T04:19:51	Jocelyn Larouche	low 4M	224640	2246400	6	-	MISSED FACTOR!	-	-	0.041	-	-	2.631%
2017-03-11T20:20:08	Jocelyn Larouche	low 4M	269568	2695680	6	-	MISSED FACTOR!	-	-	0.050	-	-	2.825%
2018-08-29T19:49:36	mikr	MSI	3000000	3000000			43038535740662936130082961071	29	95.120	0.370	0.529	0.740	3.368%
2021-11-20T13:50:22	Jocelyn Larouche	Manual testing	3109697	3109697		-	skipped known factor: 43038535740662936130082961071	-	-	0.384	-	-	3.407%
2021-12-08T12:48:17	Jocelyn Larouche	Manual testing	3109697	31096970	12	-	skipped known factor: 43038535740662936130082961071	-	-	0.572	-	-	6.066%
2021-12-21T19:29:55	Jocelyn Larouche	Manual testing	3109697	139847400		-	skipped known factor: 43038535740662936130082961071	-	-	1.303	-	-	7.839%
2021-12-22T09:19:43	Jocelyn Larouche	Manual testing	3109697	668289930		-	skipped known factor: 43038535740662936130082961071	-	-	4.856	-	-	9.701%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-02-13T15:33:00	Sturle Sunde	gollumilla.ifi	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-20T19:21:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-03T08:41:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.631	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.202	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.403	-	-
2021-01-03T02:39:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.403	-	-
2017-04-11T13:39:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.806	-	-
2021-02-25T15:38:26	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.61	-	-
2022-01-09T11:52:12	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.22	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.753 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:	1.753 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		15	1.753

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-23T00:39:00	Martti Järvi	Mardeni	50000	5000000						3	0.351
2011-07-21T23:21:00	sannerud.com	JimEmcLW7	50000	5000000						3	0.351
2013-12-06T04:33:00	Bruce	fx6840-21	50000	5000000						3	0.351
2016-05-18T04:14:07	remvad	home	50000	5000000						3	0.351
2017-11-14T08:14:11	Bruce	desk	50000	5000000						3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-23T00:00:00	ANONYMOUS	v4_computers	7C7DB15DF1B12109	0.265
1999-05-16T00:00:00	ANONYMOUS	v4_computers	7C7DB15DF1B12109	0.265

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-08-30T03:32:17

Oliver Kruse

GTX-2

43038535740662936130082961071

57E6D18C4233A3__

2018-09-03T17:58:15

Luigi Morelli

Pentium_G2030

43038535740662936130082961071

57E6D18C4233A3__

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 = 3109697, B2 = 668289930 (P-1 stage 2)

B1 = 3109697, B2 = 139847400 (P-1 stage 2)

B1 = 3109697, B2 = 31096970 (P-1 stage 2)

B1 = 3109697 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 269568, B2 = 2695680 (P-1 stage 2)

B1 = 224640, B2 = 2246400 (P-1 stage 2)

B1 = 100000, B2 = 4250000 (P-1 stage 2)

B1 = 269568 (P-1 stage 1)

B1 = 224640 (P-1 stage 1)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 187200 (P-1 stage 1)

B1 = 156000 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-09T11:52:12+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