M3461099 Mersenne number exponent details

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M3461099

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is 2 ^3461099 - 1

has 1041895 decimal digits

takes 0.364 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	A63B2836E2FB1BF2	double-checked
PRP	DD7D7321060628E9	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	34.4939	68.1159%	20000000	1000000000	11.1771	11.6147%	45.6710	71.8192%	3.7032%
PrimeNet	2⁶⁰	0.0444	63.3333%	15000	280000	0.0045	2.9030%	0.0489	64.3978%	1.0644%
GPU72	2⁶⁴	1.0284	65.6250%	19000	340000	0.0056	1.8559%	1.0339	66.2630%	0.6380%
Difference	+5	+33.4655	+2.4909%	+19981000	+999660000	+11.1715	+9.7589%	+44.6370	+5.5562%	+5.5562%

Known prime factors (1 factor, 77.8 bits, 0.00224876% 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
3461099	268996883125763533002839	24	77.832	38860038838207681 4111 × 9452697357871	2021-10-27	4111	9452697357871	16,540	78,431	146,487

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:09:00	Carsten Kossendey	leela	20000	235000		-		-	-	0.005	-	-	0.806%
2011-11-08T00:47:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.687%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78544	78544		-		-	-	0.012	-	-	0.653%
2014-09-22T21:30:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.164%
2021-03-05T07:09:22	axn	Manual testing	20000000	1000000000		-		-	-	11.18	-	-	11.615%
2022-04-10T23:56:42	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.997%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2006-04-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-21T17:06:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-30T14:55:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.089	-	-
2012-08-18T15:35:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.461	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.284	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.567	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.080	-	-
2015-04-18T18:04:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.159	-	-
2017-02-09T04:36:24	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.318	-	-
2019-02-11T13:34:46	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.636	-	-
2021-01-07T01:43:23	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.27	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.828 GHz-days
Estimated T-Level:	2.250

Digits	B1	Curves	Complete	FacMiss
20	11000	45 / 100	0.450	63.619%
25	50000	45 / 280	0.161	85.129%

New Calculation Method

Total ECM effort:	6.828 GHz-days
Estimated T-Level:	2.250

Digits	B1	Complete	FacMiss
20	11000	1.760	17.211%
25	50000	0.163	84.982%
30	250000	0.010	98.977%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.295
50000	6700000	268996883125763533002839	2	0.340
50000	6750000		7	1.193

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-12T15:31:00	Net_Force	Vista64	50000	5000000						3	0.441
2012-02-11T21:16:00	CuBr	H0E2035EE	50000	5000000						3	0.441
2015-02-26T02:54:00	joe b.	Pandora	50000	5000000						3	0.441
2016-12-28T02:44:38	Alexandr	zrhenjq123	50000	5000000						3	0.441
2019-06-16T02:44:31	Corey	Computer	50000	5000000						3	0.441
2021-03-30T06:33:04	Zenzoma	AMD3970X	50000	5000000						7	1.030
2021-05-29T16:59:27	kutens	terra	50000	6750000						7	1.193
2021-07-02T23:06:55	daveward2005	Davy	50000	5000000						7	1.030
2021-08-19T18:56:33	GAN	KL-SCH07	50000	5000000						7	1.030
2021-10-27T00:06:48	kutens	spica	50000	6700000	268996883125763533002839	77.832	2	2	1476807936763963	2	0.340

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	A63B2836E2FB1BF2	0.364
1999-09-22T00:00:00	ANONYMOUS	v4_computers	A63B2836E2FB1BF2	0.364
2006-04-14T00:00:00	ANONYMOUS	v4_computers	A63B2836E2FB1BF2	0.364

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-28T01:06:54

kutens

terra

268996883125763533002839

DD7D7321060628E9

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 = 20000000, B2 = 1000000000 (P-1 stage 2)

B1 = 20000000 (P-1 stage 1)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 78544 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 235000 (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

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T23:56:42+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