M5 984 971 Mersenne number exponent details

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M5984971

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>>>

is 2 ^5984971 - 1

has 1801656 decimal digits

takes 1.061 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	67B7A64F079DC880	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	159.7892	68.0556%	6200000	6490797390	92.3812	11.3051%	252.1704	71.6669%
Target	2⁶⁶	2.4676	65.1515%	40000	800000	0.0209	2.3468%	2.4885	65.9693%
Difference	+6	+157.3216	+2.9040%	+6160000	+6489997390	+92.3603	+8.9583%	+249.6819	+5.6976%

Known prime factors (1 factor, 130.9 bits, 0.00218675% 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
5984971	2498533603384872403644248087761147526423	40	130.876	208733977439896734975344750021441 13 × 331 × 4919 × 89627 × 440941 × 4420627 × 56447117	2023-01-25	4420627	56447117	2.336e+10	1.8644	2.3119

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-11-05	ANONYMOUS	v4_computers	30000	360000		-		-	-	0.012	-	-	0.752%
2001-04-08	MadPoo	v4_computers	25000	212500		-		-	-	0.009	-	-	0.594%
2010-10-06	Squeeky_Squirrel	P4_2600	70000	1155000		-		-	-	0.033	-	-	1.356%
2020-01-03	Aaron Haviland	Manual testing	325000	7475000	12	-		-	-	0.184	-	-	2.912%
2022-08-31	Wentao Huang	Manual testing	720000	284900070		-		-	-	4.164	-	-	6.129%
2023-01-25	Sid & Andy	Pterodactyl	6200000	6490797390			2498533603384872403644248087761147526423	40	130.876	92.38	2.121	184.8	11.305%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-16	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.051	-	-
1998-06-01	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.103	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.164	-	-
2014-10-04	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.328	-	-
2014-10-04	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.624	-	-
2015-09-30	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.249	-	-
2016-06-18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.497	-	-
2018-04-11	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.994	-	-
2020-06-05	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	9.99	-	-
2021-08-18	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	19.98	-	-
2021-08-23	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	39.95	-	-
2021-10-11	SRBase	Manual testing	2⁷¹	2⁷²		-	-	79.91	-	-

ECM factoring results:

Total ECM effort:	2.425 GHz-days
Estimated T-Level:	1.731

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	2.425

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-07-10	kagakubu	morilab_1	50000	5000000						3	0.808
2016-05-21	Bruce	Desk8	50000	5000000						3	0.808
2019-10-07	IanGlencross	glenx24	50000	5000000						3	0.808

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-02	ANONYMOUS	v4_computers	67B7A64F079DC880	1.061
2001-05-20	MadPoo	v4_computers	67B7A64F079DC880	1.061

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-01-31

Perig

brollach

2498533603384872403644248087761147526423

59C8F96BE5B531E8

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 = 6200000, B2 = 6490797390 (P-1 stage 2)

B1 = 720000, B2 = 284900070 (P-1 stage 2)

B1 = 6200000 (P-1 stage 1)

B1 = 720000 (P-1 stage 1)

B1 = 325000, B2 = 7475000 (P-1 stage 2)

B1 = 325000 (P-1 stage 1)

B1 = 70000, B2 = 1155000 (P-1 stage 2)

B1 = 70000 (P-1 stage 1)

B1 = 30000, B2 = 360000 (P-1 stage 2)

B1 = 25000, B2 = 212500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 66

TF double-checked to: 67.7

ECM T-Level=1.73 ~= -11-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