M3 117 911 Mersenne number exponent details

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M3117911

<<<

>>>

is 2 ^3117911 - 1

has 938585 decimal digits

takes 0.265 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	412CC347B5DFF267	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	76.6381	68.5714%	8900000	22840692420	154.6143	14.1971%	231.2523	73.0334%
Target	2⁶⁴	1.1416	65.6250%	14000	240000	0.0032	1.5088%	1.1448	66.1437%
Difference	+6	+75.4965	+2.9464%	+8886000	+22840452420	+154.6110	+12.6882%	+230.1075	+6.8897%

Known prime factors (1 factor, 125.6 bits, 0.00402776% 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
3117911	63671608794629485321298180852470139537	38	125.582	10210619994385581455227262877688 2³ × 15083 × 24677 × 3050389 × 6521513 × 172376653	2023-03-13	6521513	172376653	5.761e+10	1.9200	2.1647

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.162%
2009-07-03	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.554%
2011-08-26	Squeeky_Squirrel	T7500_2200	105000	2126250		-		-	-	0.027	-	-	2.019%
2016-09-29	Squeeky_Squirrel	i5-5250U_1600	195000	5460000	12	-		-	-	0.059	-	-	2.832%
2016-10-03	Jocelyn Larouche	low 4M	105000	2551500	6	-		-	-	0.029	-	-	2.109%
2018-07-15	Jocelyn Larouche	low 4M	670000	2680000		-		-	-	0.096	-	-	2.797%
2018-07-16	Jocelyn Larouche	low 4M	670000	4020000		-		-	-	0.105	-	-	3.118%
2018-10-25	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	6.834%
2022-09-27	Jocelyn Larouche	Manual testing	1000000	118249950		-		-	-	0.912	-	-	6.272%
2022-10-29	Jocelyn Larouche	Manual testing	1000000	265074810		-		-	-	1.899	-	-	7.042%
2023-03-13	Sid & Andy	Barrel_Of_Monkeys	8900000	22840692420			63671608794629485321298180852470139537	38	125.582	154.6	0.531	309.2	14.197%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-12	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-18	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-07	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.315	-	-
2015-02-07	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.630	-	-
2015-02-07	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.198	-	-
2015-06-11	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.397	-	-
2017-04-14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.793	-	-
2019-01-21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.59	-	-
2020-11-27	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	19.17	-	-
2020-11-27	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	38.35	-	-

ECM factoring results:

Total ECM effort:	13.568 GHz-days
Estimated T-Level:	22.048

Digits	B1	Complete	FacMiss
20	11000	4.429	1.192%
25	50000	0.410	66.397%
30	250000	0.026	97.447%
35	1000000	0.001	99.879%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	100	11.69
50000	6599832	7	0.934
50000	6708363	7	0.942

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-25	Jürgen Decker	Q9550_home	50000	5000000						3	0.351
2011-07-22	Boots	Technomicron2	50000	5000000						3	0.351
2014-02-09	Richard Kint	xps	50000	5000000						3	0.351
2016-05-24	Richard Kint	xps	50000	5000000						3	0.351
2017-11-29	Volki		50000	5000000						3	0.351
2020-11-11	IanGlencross	glenx24	50000	5000000						7	0.818
2020-12-18	daveward2005	Dave2	50000	5000000						7	0.818
2021-01-18	Zenzoma	AM3700X_1	50000	5000000						7	0.818
2021-02-17	Zenzoma	AMD3970X	50000	5000000						7	0.818
2021-03-30	mnd9	75204	50000	5000000						7	0.818
2021-04-28	Zenzoma	AM3700X_1	50000	5000000						7	0.818
2021-06-17	daveward2005	d12436	50000	5000000						7	0.818
2021-07-28	daveward2005	d12436	50000	5000000						7	0.818
2021-09-25	daveward2005	Dave2	50000	5000000						7	0.818
2021-12-28	RIHATEC	i7-3770K	50000	5000000						7	0.818
2022-04-14	J.R. Allen	lapasus	50000	6599832						7	0.934
2022-07-28	C.D.B.	i7-6850K	50000	5000000						7	0.818
2022-10-22	MarkS	desktop-i7	50000	6708363						7	0.942
2023-01-10	Jonathan Webb	do-primes-2	50000	5000000						8	0.935

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Themos Tsikas		412CC347B5DFF267	0.265
1999-05-16	ANONYMOUS	v4_computers	412CC347B5DFF267	0.265

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-03-15

Naegi Makoto

5950X

63671608794629485321298180852470139537

C090BDEDCF3F31CE

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 = 8900000, B2 = 22840692420 (P-1 stage 2)

B1 = 1000000, B2 = 265074810 (P-1 stage 2)

B1 = 8900000 (P-1 stage 1)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 118249950 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 670000, B2 = 4020000 (P-1 stage 2)

B1 = 670000, B2 = 2680000 (P-1 stage 2)

B1 = 670000 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

B1 = 105000, B2 = 2551500 (P-1 stage 2)

B1 = 105000, B2 = 2126250 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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=22.05 ~= 57-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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