M3650533 Mersenne number exponent details

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M3650533

<<<

>>>

is 2 ^3650533 - 1

has 1098920 decimal digits

takes 0.383 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	9DF1A448CF24CD9E	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	2⁷⁰	65.4564	68.5714%	30000000	600000000	9.2981	10.3748%	74.7545	71.8321%	3.2607%
PrimeNet	2⁶⁰	0.0421	63.3333%	16000	320000	0.0050	3.0765%	0.0470	64.4614%	1.1280%
GPU72	2⁶⁴	0.9750	65.6250%	22000	400000	0.0065	2.0363%	0.9815	66.3250%	0.7000%
Difference	+6	+64.4814	+2.9464%	+29978000	+599600000	+9.2916	+8.3386%	+73.7730	+5.5071%	+5.5071%

Known prime factors (1 factor, 71.0 bits, 0.00194382% 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
3650533	2296126412300877865831	22	70.960	314491940259255 3² × 5 × 11 × 635337253049	2021-08-30	11	635337253049	128.62	5,271.5	9,845.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:46:00	Carsten Kossendey	leela	20000	250000		-		-	-	0.005	-	-	0.713%
2012-01-29T08:56:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	1.877%
2016-06-13T00:04:28	Jocelyn Larouche	Manual testing	108000	3285000	6	-		-	-	0.043	-	-	2.305%
2016-12-29T20:13:45	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.775%
2017-01-30T01:30:52	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	0.897%
2017-03-02T20:51:39	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.477%
2020-09-05T14:31:06	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.375%
2022-03-04T04:19:05	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.621%
2022-03-22T11:09:09	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.663%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:35	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-10T06:03:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-16T12:42:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.084	-	-
2012-06-05T02:30:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.437	-	-
2016-02-23T16:29:35	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.269	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.538	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.024	-	-
2015-10-20T08:54:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.047	-	-
2016-12-28T15:57:35	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.094	-	-
2019-02-13T05:38:53	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	8.188	-	-
2020-11-08T02:44:54	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.38	-	-
2020-11-17T11:57:39	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.716 GHz-days
Estimated T-Level:	1.250

Digits	B1	Curves	Complete	FacMiss
20	11000	25 / 100	0.250	77.782%
25	50000	25 / 280	0.089	91.444%

New Calculation Method

Total ECM effort:	3.716 GHz-days
Estimated T-Level:	1.250

Digits	B1	Complete	FacMiss
20	11000	0.806	44.644%
25	50000	0.073	92.971%
30	250000	0.004	99.552%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.270
50000	5000000	2296126412300877865831	3	0.446

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-16T08:37:00	Smurgs	Praca	50000	5000000						3	0.446
2012-06-13T19:22:00	Lukasz Wrobel	u-w	50000	5000000						3	0.446
2015-09-16T06:14:00	driveByUpgrades	Build_4	50000	5000000						3	0.446
2017-05-11T11:59:01	Conductor	NataW	50000	5000000						3	0.446
2020-11-19T02:29:07	axn	Manual testing	50000	5000000						10	1.486
2021-08-30T13:12:28	daveward2005	Dave2	50000	5000000	2296126412300877865831	70.960	3	2	2363717217737341	3	0.446

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-29T00:00:00	ANONYMOUS	v4_computers	27F147BA5F5F05__	0.383

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-09-06T18:57:37

Yizhe Huang

desk

2296126412300877865831

9DF1A448CF24CD9E

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 = 30000000, B2 = 600000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 241228, B2 = 2412280 (P-1 stage 2)

B1 = 108000, B2 = 3285000 (P-1 stage 2)

B1 = 241228 (P-1 stage 1)

B1 = 90000, B2 = 1642500 (P-1 stage 2)

B1 = 167520 (P-1 stage 1)

B1 = 129600 (P-1 stage 1)

B1 = 108000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 250000 (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:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-22T11:09:09+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