M3 220 603 Mersenne number exponent details

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M3220603

<<<

>>>

is 2 ^3220603 - 1

has 969499 decimal digits

takes 0.274 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	13D572E518388DCB	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	74.1944	68.5714%	8700000	22323365610	151.1125	14.1790%	225.3069	73.0277%
Target	2⁶⁴	1.1052	65.6250%	16000	260000	0.0036	1.6177%	1.1088	66.1811%
Difference	+6	+73.0892	+2.9464%	+8684000	+22323105610	+151.1089	+12.5613%	+224.1981	+6.8466%

Known prime factors (1 factor, 134.3 bits, 0.00417127% 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
3220603	27565379526468140340686968486919020339927	41	134.340	4279537019382416948112972708359121 3 × 7 × 13 × 1601 × 848273 × 1196863 × 2903387 × 3321680029	2023-03-13	2903387	3321680029	5.445e+10	22.673	41.714

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03	Carsten Kossendey	durandal	15000	191250		-		-	-	0.003	-	-	0.570%
2011-09-04	harlee	P4_2600	60000	1035000		-		-	-	0.014	-	-	1.480%
2014-06-09	Jocelyn Larouche	Manual testing	79929	79929		-		-	-	0.010	-	-	0.561%
2014-09-29	Jocelyn Larouche	Manual testing	99858	99858		-		-	-	0.012	-	-	0.647%
2015-12-15	Squeeky_Squirrel	P4_2600	155000	3952500	6	-		-	-	0.045	-	-	2.539%
2016-04-19	Jocelyn Larouche	Manual testing	435447	12938233	6	-		-	-	0.138	-	-	3.862%
2020-03-06	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	7.481%
2023-03-13	Sid & Andy	Hockey_Puck	8700000	22323365610			27565379526468140340686968486919020339927	41	134.340	151.1	0.548	302.2	14.179%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-29	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-05	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-09-19	markr	oldgamer	2⁶¹	2⁶²		-	-	0.095	-	-
2013-01-03	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.305	-	-
2015-02-15	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.610	-	-
2015-02-15	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.160	-	-
2015-06-24	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.320	-	-
2017-03-20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.641	-	-
2018-12-24	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.281	-	-
2021-02-01	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.56	-	-
2022-05-25	TJAOI	Manual testing	2⁶⁹	2⁷⁰		-	-	37.12	-	-

ECM factoring results:

Total ECM effort:	14.184 GHz-days
Estimated T-Level:	21.842

Digits	B1	Complete	FacMiss
20	11000	3.955	1.917%
25	50000	0.368	69.191%
30	250000	0.023	97.695%
35	1000000	0.001	99.891%

ECM Summary

B1	B2	curves	GHz-days
50000	3550000	7	0.717
50000	4900000	7	0.816
50000	5000000	57	6.703
50000	6350000	14	1.845
50000	7000000	7	0.970
50000	31130190	8	3.134

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-18	Stun	Core2	50000	5000000						3	0.353
2011-09-07	GrunwalderGIMP	vangelis	50000	5000000						3	0.353
2014-05-11	Brett Walker		50000	5000000						3	0.353
2016-08-09	f0rteOC	Fortissimo	50000	5000000						3	0.353
2018-10-01	IanGlencross	glenx24	50000	5000000						3	0.353
2020-12-25	Zenzoma	AM3700X_1	50000	5000000						7	0.823
2021-01-25	Zenzoma	AM3700X_1	50000	5000000						7	0.823
2021-02-23	Zenzoma	AMD3970X	50000	5000000						7	0.823
2021-03-28	Zenzoma	AMD3970X	50000	5000000						7	0.823
2021-05-20	kutens	rigel	50000	4900000						7	0.816
2021-06-26	daveward2005	d12436	50000	5000000						7	0.823
2021-08-10	daveward2005	d12436	50000	5000000						7	0.823
2021-10-19	Ahmed Azhad	c5.azf2	50000	6350000						7	0.922
2022-02-01	saemiller	ASUS_Laptop	50000	6350000						7	0.922
2022-07-17	tonyw	Doh_002	50000	7000000						7	0.970
2022-08-31	-Anonymous-		50000	3550000						7	0.717
2023-01-22	Nesowa	entropy_generator_3	50000	31130190						8	3.134

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Dax Prather		13D572E518388DCB	0.274
1998-08-24	ANONYMOUS	v4_computers	13D572E518388DCB	0.274
1999-06-26	TeraTism	v4_computers	13D572E518388DCB	0.274

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-03-15

Naegi Makoto

5950X

27565379526468140340686968486919020339927

1980F2BDAAE993A6

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 = 8700000, B2 = 22323365610 (P-1 stage 2)

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

B1 = 8700000 (P-1 stage 1)

B1 = 4000000 (P-1 stage 1)

B1 = 435447, B2 = 12938233 (P-1 stage 2)

B1 = 435447 (P-1 stage 1)

B1 = 155000, B2 = 3952500 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

B1 = 60000, B2 = 1035000 (P-1 stage 2)

B1 = 99858 (P-1 stage 1)

B1 = 79929 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (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: 67.7

ECM T-Level=21.84 ~= 56-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-03-25T13:08:14+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