M3354269 Mersenne number exponent details

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M3354269

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is 2 ^3354269 - 1

has 1009736 decimal digits

takes 0.352 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	E25A4645CD313495	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	2⁶⁸	17.7699	67.6471%	4000000	150000000	1.8206	8.7999%	19.5904	70.4941%	2.8470%
PrimeNet	2⁶⁰	0.0458	63.3333%	14000	280000	0.0043	2.8403%	0.0501	64.3748%	1.0415%
GPU72	2⁶⁴	1.0611	65.6250%	18000	300000	0.0051	1.7558%	1.0662	66.2286%	0.6036%
Difference	+4	+16.7087	+2.0221%	+3982000	+149700000	+1.8155	+7.0441%	+18.5242	+4.2655%	+4.2655%

Known prime factors (1 factor, 74.2 bits, 0.00221285% 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
3354269	22077213973250138313097	23	74.225	3290912859590292 2² × 3 × 274242738299191	2021-02-22	4	274242738299191	1,276.9	2,275,445	4,249,898

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-05T17:23:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.809%
2011-10-11T23:12:00	harlee	P4_2600	55000	907500		-		-	-	0.015	-	-	1.829%
2014-05-19T21:01:00	Jocelyn Larouche	Manual testing	74135	74135		-		-	-	0.011	-	-	0.725%
2014-09-23T20:52:00	Jocelyn Larouche	Manual testing	93270	93270		-		-	-	0.014	-	-	0.834%
2015-07-31T12:12:00	Jocelyn Larouche	Manual testing	397784	397784		-		-	-	0.061	-	-	1.759%
2015-10-07T06:14:15	Jocelyn Larouche	Manual testing	453520	453520		-		-	-	0.069	-	-	1.863%
2015-12-06T13:29:47	Jocelyn Larouche	Manual testing	498872	498872		-		-	-	0.076	-	-	1.941%
2016-05-09T02:46:00	mognuts	Stanley	20000	200000		-		-	-	0.005	-	-	0.885%
2016-06-20T03:43:46	Jocelyn Larouche	Manual testing	498872	997744		-		-	-	0.080	-	-	2.532%
2016-06-21T03:40:58	Jocelyn Larouche	Manual testing	498872	1995488	6	-		-	-	0.088	-	-	3.133%
2016-07-17T03:47:13	Jocelyn Larouche	Manual testing	498872	3990976	6	-		-	-	0.105	-	-	3.746%
2020-10-11T10:17:47	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.800%
2022-03-18T13:53:54	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.259	-	-	7.668%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-29T08:00:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-08-19T22:54:00	markr	Manual testing	2¹	2⁶²		-	-	0.183	-	-
2012-11-15T00:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.476	-	-
2016-02-23T16:29:26	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.293	-	-
2015-02-11T09:07:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.585	-	-
2015-02-11T09:07:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.114	-	-
2016-03-04T01:08:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.228	-	-
2017-03-05T04:56:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.456	-	-
2018-12-17T13:21:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.911	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.650 GHz-days
Estimated T-Level:	3.300

Digits	B1	Curves	Complete	FacMiss
20	11000	66 / 100	0.660	51.514%
25	50000	66 / 280	0.236	78.967%

New Calculation Method

Total ECM effort:	9.650 GHz-days
Estimated T-Level:	3.300

Digits	B1	Complete	FacMiss
20	11000	2.129	11.895%
25	50000	0.192	82.496%
30	250000	0.012	98.822%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.193
50000	5000000	22077213973250138313097	51	7.457

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-06T09:12:00	sasaki3	ssk_saver	50000	5000000						3	0.439
2012-02-01T02:54:00	CuBr	H0E2035EE	50000	5000000						3	0.439
2014-09-17T02:27:00	Lukasz Wrobel	v7	50000	5000000						3	0.439
2016-10-22T09:13:11	Dennis Schreiber	z400	50000	5000000						3	0.439
2019-03-30T21:38:36	furkell	furkell1	50000	5000000						3	0.439
2021-02-22T16:31:42	MarkS	desktop-i7	50000	5000000	22077213973250138313097	74.225	51	2	6783208533416628	51	7.457

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	37C61EB81F41C0__	0.352

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-02-23T15:22:58

mrh

lanai

22077213973250138313097

E25A4645CD313495

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 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 498872, B2 = 3990976 (P-1 stage 2)

B1 = 498872, B2 = 1995488 (P-1 stage 2)

B1 = 498872, B2 = 997744 (P-1 stage 2)

B1 = 498872 (P-1 stage 1)

B1 = 453520 (P-1 stage 1)

B1 = 397784 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 93270 (P-1 stage 1)

B1 = 74135 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 20000, B2 = 200000 (P-1 stage 2)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-18T13:53:54+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