M3495253 Mersenne number exponent details

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M3495253

<<<

>>>

is 2 ^3495253 - 1

has 1052176 decimal digits

takes 0.367 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	E0874DCEC1E1604F	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	34.1568	68.1159%	15000000	750000000	8.3828	11.0586%	42.5396	71.6419%	3.5259%
PrimeNet	2⁶⁰	0.0439	63.3333%	15000	300000	0.0046	2.9597%	0.0486	64.4186%	1.0852%
GPU72	2⁶⁴	1.0183	65.6250%	20000	360000	0.0059	1.9149%	1.0242	66.2833%	0.6583%
Difference	+5	+33.1385	+2.4909%	+14980000	+749640000	+8.3769	+9.1436%	+41.5154	+5.3586%	+5.3586%

Known prime factors (1 factor, 69.5 bits, 0.00198718% 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
3495253	810246330278217623711	21	69.457	115906678326035 5 × 73 × 317552543359	2021-04-21	73	317552543359	57.961	2,634.8	4,921.1

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-08T05:54:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.813%
2011-11-18T03:20:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.690%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78363	78363		-		-	-	0.012	-	-	0.653%
2014-09-05T16:48:00	HBendtz	Manual testing	615000	12000000		-		-	-	0.188	-	-	4.432%
2021-04-06T08:01:32	axn	Manual testing	15000000	750000000		-		-	-	8.383	-	-	11.059%
2022-04-10T23:56:45	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	7.004%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-19T18:07:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-14T20:49:00	markr	Manual testing	2¹	2⁶²		-	-	0.176	-	-
2012-08-18T15:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.457	-	-
2016-02-23T16:29:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.281	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.562	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.069	-	-
2016-01-06T22:34:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.138	-	-
2017-02-20T16:19:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.276	-	-
2018-07-23T16:23:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.552	-	-
2021-01-13T13:19:18	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.10	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.242 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	3.242 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.846	42.906%
25	50000	0.078	92.469%
30	250000	0.005	99.507%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.211
50000	5000000	810246330278217623711	7	1.032

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-19T10:15:00	sasaki3	ssk_saver	50000	5000000						3	0.442
2012-03-10T07:54:00	Smurgs	Praca	50000	5000000						3	0.442
2015-05-28T18:39:00	Pool Party	St.P.p	50000	5000000						3	0.442
2017-01-26T21:20:03	Lelikoid	QH	50000	5000000						3	0.442
2019-07-19T10:40:58	nokno	leo234	50000	5000000						3	0.442
2021-04-21T17:41:46	Zenzoma	AM3700X_1	50000	5000000	810246330278217623711	69.457	7	2	5938569204455783	7	1.032

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	E0874DCEC1E1604F	0.367

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-21T21:25:43

mikr

Nitron

810246330278217623711

89D8C2778C26EAE8

2021-04-22T14:29:55

XZT

N4640G2

810246330278217623711

89D8C2778C26EAE8

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

B1 = 615000, B2 = 12000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 615000 (P-1 stage 1)

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

B1 = 78363 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T23:56:45+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