M3524903 Mersenne number exponent details

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M3524903

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>>>

is 2 ^3524903 - 1

has 1061102 decimal digits

takes 0.370 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	5702E6CB0ACA5DFB	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	2⁷²	271.3078	69.4444%	4000000	324000000	3.2643	7.2117%	274.5721	71.6480%	2.2036%
PrimeNet	2⁶⁰	0.0436	63.3333%	15000	300000	0.0046	2.9641%	0.0482	64.4202%	1.0869%
GPU72	2⁶⁴	1.0098	65.6250%	20000	360000	0.0059	1.9179%	1.0156	66.2843%	0.6593%
Difference	+8	+270.2980	+3.8194%	+3980000	+323640000	+3.2584	+5.2938%	+273.5564	+5.3638%	+5.3638%

Known prime factors (1 factor, 102.9 bits, 0.00291834% 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
3524903	9259329234631759454770385264417	31	102.869	1313416175513448094141936 2⁴ × 19 × 211 × 173651 × 946859 × 124532791	2022-01-13	946859	124532791	4.263e+10	1.1696	1.9299

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:56:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.514%
2011-11-21T02:02:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.137%
2014-08-07T10:52:00	Jocelyn Larouche	Manual testing	78209	78209		-		-	-	0.012	-	-	0.417%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	96418	96418		-		-	-	0.015	-	-	0.480%
2015-10-21T03:03:34	Squeeky_Squirrel	P4_2600	170000	4590000	6	-		-	-	0.063	-	-	2.154%
2017-04-27T04:16:43	Jocelyn Larouche	low 4M	340000	3400000	6	-		-	-	0.077	-	-	2.266%
2021-01-08T23:20:54	Dylan Delgado	Manual testing	1600000	50000000	12	-		-	-	0.645	-	-	4.880%
2022-01-13T03:17:46	mikr	MSI	4000000	324000000			9259329234631759454770385264417	31	102.869	3.264	0.740	6.529	7.212%
2022-02-25T17:22:20	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.030	-	-	0.751%
2022-04-30T16:38:16	Jocelyn Larouche	Manual testing	500000	145208700		-		-	-	1.277	-	-	4.951%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-09-14T12:17:37	ArtyomP	axioo	50000	2500000	2	7			-	-	0.032
2021-09-14T12:37:10	ArtyomP	axioo	50000	2500000	6	5			-	-	0.032

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:32	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-18T05:52:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-02T00:58:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.087	-	-
2012-06-20T01:19:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.453	-	-
2016-02-23T16:29:32	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.278	-	-
2015-01-27T16:52:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.557	-	-
2015-01-27T16:52:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.060	-	-
2016-03-03T23:02:53	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.120	-	-
2017-01-10T19:01:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.240	-	-
2018-11-26T14:19:29	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.480	-	-
2021-01-19T04:11:55	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.96	-	-
2021-03-18T17:15:05	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	33.92	-	-
2021-03-18T17:15:06	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	67.84	-	-
2021-03-19T23:55:48	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	135.7	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.677 GHz-days
Estimated T-Level:	2.150

Digits	B1	Curves	Complete	FacMiss
20	11000	43 / 100	0.430	64.910%
25	50000	43 / 280	0.154	85.740%

New Calculation Method

Total ECM effort:	6.677 GHz-days
Estimated T-Level:	2.150

Digits	B1	Complete	FacMiss
20	11000	1.418	24.214%
25	50000	0.129	87.910%
30	250000	0.008	99.208%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	4.281
50000	6750000		14	2.396

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-26T19:49:00	abc	C30D35CA5	50000	5000000						3	0.443
2012-03-28T23:00:00	Smurgs	Praca	50000	5000000						3	0.443
2015-05-29T20:20:00	Helmut Kirrmaier	TECRA	50000	5000000						3	0.443
2017-02-16T17:17:00	Bruce	agent86	50000	5000000						3	0.443
2019-09-07T14:28:50	Idgo	Pentium_Desktop	50000	5000000						3	0.443
2021-05-09T16:14:51	Anton Evers	windows_laptop	50000	5000000						7	1.033
2021-06-22T15:37:09	Stef42	AMD-DESKTOP	50000	6750000						7	1.198
2021-08-09T15:47:17	nordi	sweet16	50000	6750000						7	1.198
2021-11-05T23:09:40	GAN	KL-SCH07	50000	5000000						7	1.033

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2198D7CE02096D__	0.370

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-01-19T01:17:04

kutens

terra

9259329234631759454770385264417

5702E6CB0ACA5DFB

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 = 4000000, B2 = 324000000 (P-1 stage 2)

B1 = 500000, B2 = 145208700 (P-1 stage 2)

B1 = 1600000, B2 = 50000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1600000 (P-1 stage 1)

B1 = 340000, B2 = 3400000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 170000, B2 = 4590000 (P-1 stage 2)

B1 = 340000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 170000 (P-1 stage 1)

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

B1 = 96418 (P-1 stage 1)

B1 = 78209 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 245000 (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:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2022-04-30T16:38:16+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