M3 324 491 Mersenne number exponent details

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M3324491

<<<

>>>

is 2 ^3324491 - 1

has 1000772 decimal digits

takes 0.349 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	3B4C5D35702F836A	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁰	71.8759	68.5714%	6300000	22713580890	189.3662	13.8856%	261.2420	72.9355%
Target	2⁶⁴	1.0706	65.6250%	17000	1500000	0.0149	1.7246%	1.0855	66.2178%
Difference	+6	+70.8052	+2.9464%	+6283000	+22712080890	+189.3513	+12.1610%	+260.1565	+6.7176%

Known prime factors (1 factor, 132.4 bits, 0.00398207% 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
3324491	7102601511883504796597083238581761018769	40	132.384	1068223904333551331105586274497624 2³ × 3 × 19 × 41 × 1733 × 31849 × 286927 × 2106901 × 1712393941	2023-05-09	2106901	1712393941	3.997e+10	14.511	26.537

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-21	ANONYMOUS	v4_computers	75000	1000000		-		-	-	0.019	-	-	1.556%
2014-09-23	Jocelyn Larouche	Manual testing	94306	94306		-		-	-	0.014	-	-	0.628%
2015-12-05	HBendtz	Manual testing	500000	12000000	12	-		-	-	0.172	-	-	3.892%
2020-05-03	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	7.505%
2023-05-08	Jocelyn Larouche	Manual testing	1000000	962851890		-		-	-	8.133	-	-	8.358%
2023-05-09	Sid & Andy	Magic_8_Ball	6300000	22713580890			7102601511883504796597083238581761018769	40	132.384	189.4	0.698	378.7	13.886%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-11	S00858	v4_computers	2¹	2⁶⁰		-	-	0.046	-	-
2002-02-10	S00858	v4_computers	2¹	2⁶⁰		-	-	0.046	-	-
2009-03-29	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-09-06	markr	oldgamer	2⁶¹	2⁶²		-	-	0.092	-	-
2012-08-25	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.480	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.295	-	-
2015-02-11	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.591	-	-
2015-02-11	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.124	-	-
2016-03-02	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.248	-	-
2017-02-27	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.496	-	-
2018-11-19	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.991	-	-
2021-08-05	MadPoo	Manual testing	2⁶⁸	2⁶⁹		-	-	17.98	-	-
2022-08-30	TJAOI	Manual testing	2⁶⁹	2⁷⁰		-	-	35.96	-	-

ECM factoring results:

Total ECM effort:	13.257 GHz-days
Estimated T-Level:	21.566

Digits	B1	Complete	FacMiss
20	11000	3.381	3.400%
25	50000	0.313	73.104%
30	250000	0.020	98.036%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	50	7.299
50000	6750000	7	1.182
50000	6800000	14	2.374
50000	6900000	7	1.196
50000	7000000	7	1.205

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-29	James Hintz	06_060209	50000	5000000						3	0.438
2011-11-06	sannerud.com	Jens2010	50000	5000000						3	0.438
2014-08-15	S36049	Wolle4	50000	5000000						3	0.438
2016-10-05	f0rteOC	Fortissimo	50000	5000000						3	0.438
2019-03-10	LordJulius	BlackboxNouveau	50000	5000000						3	0.438
2021-02-04	lycorn	colab_A_1	50000	6800000						7	1.187
2021-03-10	daveward2005	Dave2	50000	5000000						7	1.022
2021-04-17	Zenzoma	AM3700X_1	50000	5000000						7	1.022
2021-06-08	Stef42	AMD-DESKTOP	50000	6750000						7	1.182
2021-07-24	kutens	arcturus	50000	6800000						7	1.187
2021-09-28	Sergey Nosov	TS140-02	50000	5000000						7	1.022
2021-12-30	daveward2005	Dave2	50000	5000000						7	1.022
2022-04-14	voidf	ATRI	50000	7000000						7	1.205
2022-07-29	Sergey Nosov	TS140-02	50000	5000000						7	1.022
2022-10-26	mikr	P075	50000	6900000						7	1.196

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08	S00858	v4_computers	3B4C5D35702F836A	0.349
2001-12-22	ANONYMOUS	v4_computers	3B4C5D35702F836A	0.349
2002-02-10	S00858	v4_computers	3B4C5D35702F836A	0.349
2017-06-11	kkmrkkblmbrbk	old	3B4C5D35702F836A	0.349

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-05-09

Naegi Makoto

5950X

7102601511883504796597083238581761018769

AB94C6E36CB15C26

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 = 6300000, B2 = 22713580890 (P-1 stage 2)

B1 = 1000000, B2 = 962851890 (P-1 stage 2)

B1 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 6300000 (P-1 stage 1)

B1 = 4000000 (P-1 stage 1)

B1 = 500000, B2 = 12000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 75000, B2 = 1000000 (P-1 stage 2)

B1 = 94306 (P-1 stage 1)

B1 = 75000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

this exponent TF target: 64

TF double-checked to: 67.9

ECM T-Level=21.57 ~= 55-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-09-25T11:53:03+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