M3433453 Mersenne number exponent details

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M3433453

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>>>

is 2 ^3433453 - 1

has 1033573 decimal digits

takes 0.361 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	469AE5AB1628CFA5	double-checked
PRP	4B26F50B6D8291EB	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	34.7716	68.1159%	1000000	114656850	1.0953	6.8892%	35.8670	70.3125%	2.1966%
PrimeNet	2⁶⁰	0.0447	63.3333%	15000	280000	0.0045	2.8989%	0.0492	64.3963%	1.0629%
GPU72	2⁶⁴	1.0367	65.6250%	19000	340000	0.0056	1.8531%	1.0422	66.2620%	0.6370%
Difference	+5	+33.7350	+2.4909%	+981000	+114316850	+1.0898	+5.0361%	+34.8247	+4.0505%	+4.0505%

Known prime factors (1 factor, 70.3 bits, 0.00204660% 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
3433453	1422488484569934940183	22	70.269	207151297042647 3 × 23 × 3002192710763	2021-03-23	23	3002192710763	126.99	24,910	46,525

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2010-09-23T18:43:00	Rob_Dee	twopc	10000	20000		-		-	-	0.002	-	-	0.216%
2010-09-23T19:55:00	Rob_Dee	twopc	20000	30000		-		-	-	0.003	-	-	0.322%
2010-09-23T22:32:00	Rob_Dee	twopc	30000	40000		-		-	-	0.005	-	-	0.407%
2010-09-24T05:01:00	Rob_Dee	twopc	40000	50000		-		-	-	0.006	-	-	0.480%
2010-09-24T18:14:00	Rob_Dee	twopc	50000	60000		-		-	-	0.008	-	-	0.545%
2010-09-24T19:40:00	Rob_Dee	twopc	60000	70000		-		-	-	0.009	-	-	0.604%
2010-09-24T20:32:00	Rob_Dee	twopc	70000	80000		-		-	-	0.011	-	-	0.658%
2010-09-24T21:21:00	Rob_Dee	twopc	80000	90000		-		-	-	0.012	-	-	0.709%
2010-09-25T06:19:00	Rob_Dee	twopc	90000	100000		-		-	-	0.014	-	-	0.756%
2010-09-25T23:33:00	Rob_Dee	twopc	100000	200000		-		-	-	0.016	-	-	1.081%
2010-09-26T05:30:00	Rob_Dee	twopc	100000	400000		-		-	-	0.018	-	-	1.418%
2010-09-26T19:13:00	Rob_Dee	twopc	100000	600000		-		-	-	0.019	-	-	1.622%
2010-09-26T20:31:00	Rob_Dee	twopc	100000	800000		-		-	-	0.021	-	-	1.769%
2010-09-27T04:16:00	Rob_Dee	twopc	100000	1000000		-		-	-	0.023	-	-	1.885%
2014-09-15T17:58:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.160%
2022-02-12T19:37:11	Jocelyn Larouche	Manual testing	1000000	114656850		-		-	-	1.095	-	-	6.889%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:29	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-24T06:24:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-08T01:15:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.089	-	-
2012-08-18T15:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.465	-	-
2016-02-23T16:29:29	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.286	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.572	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.088	-	-
2015-04-13T08:56:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.176	-	-
2017-02-05T22:59:57	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.353	-	-
2022-01-22T13:05:29	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.706	-	-
2018-09-24T14:19:06	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.706	-	-
2021-01-01T04:52:50	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.790 GHz-days
Estimated T-Level:	0.950

Digits	B1	Curves	Complete	FacMiss
20	11000	19 / 100	0.190	82.617%
25	50000	19 / 280	0.068	93.428%

New Calculation Method

Total ECM effort:	2.790 GHz-days
Estimated T-Level:	0.950

Digits	B1	Complete	FacMiss
20	11000	0.613	54.178%
25	50000	0.055	94.611%
30	250000	0.003	99.659%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.203
50000	5000000	1422488484569934940183	4	0.587

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-03T16:49:00	Gerry Snyder	blu	50000	5000000						3	0.441
2012-01-19T20:44:00	Smurgs	Praca	50000	5000000						3	0.441
2015-01-23T00:15:00	S36049	Wolle6	50000	5000000						3	0.441
2016-12-13T05:55:12	f0rteOC	Fortissimo	50000	5000000						3	0.441
2019-05-28T06:31:55	pfrakes	Q8400-linux-4	50000	5000000						3	0.441
2021-03-23T21:29:53	mnd9	75202b	50000	5000000	1422488484569934940183	70.269	4	2	5401518195086842	4	0.587

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-04T00:00:00	ANONYMOUS	v4_computers	469AE5AB1628CFA5	0.361
1999-07-04T00:00:00	ANONYMOUS	v4_computers	469AE5AB1628CFA5	0.361

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-03-25T03:23:36

Hyeonseung Kwon

1422488484569934940183

4B26F50B6D8291EB

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 = 1000000, B2 = 114656850 (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 = 100000, B2 = 1000000 (P-1 stage 2)

B1 = 100000, B2 = 800000 (P-1 stage 2)

B1 = 100000, B2 = 600000 (P-1 stage 2)

B1 = 100000, B2 = 400000 (P-1 stage 2)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000, B2 = 100000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 80000, B2 = 90000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 70000, B2 = 80000 (P-1 stage 2)

B1 = 70000 (P-1 stage 1)

B1 = 60000, B2 = 70000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 50000, B2 = 60000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 40000, B2 = 50000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

B1 = 30000, B2 = 40000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000, B2 = 30000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 10000, B2 = 20000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

10⁰

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10²

10³

10⁴

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10⁶

10⁷

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10¹³

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-12T19:37:11+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