M4968559 Mersenne number exponent details

Residue

Status

L-L

E21CAB626311547F

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁴	770.0152	68.9189%	50000000	160135168050	1,763.0264	15.2398%	2,533.0415	73.6556%
Target	2⁶⁵	1.4684	64.6154%	34000	700000	0.0141	2.4134%	1.4825	65.4694%
Difference	+9	+768.5468	+4.3035%	+49966000	+160134468050	+1,763.0122	+12.8263%	+2,531.5590	+8.1862%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁴

770.0152

68.9189%

50000000

160135168050

1,763.0264

15.2398%

2,533.0415

73.6556%

Target

2⁶⁵

1.4684

64.6154%

34000

700000

0.0141

2.4134%

1.4825

65.4694%

Difference

+768.5468

+4.3035%

+49966000

+160134468050

+1,763.0122

+12.8263%

+2,531.5590

+8.1862%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4968559	2024609142059135603124721	25	80.744	203742085185980040 2³ × 3 × 5 × 7 × 32909 × 7370327309	2022-10-04	32909	7370327309	89,606	80.713	150.74
4968559	2231728093642762521609553280152576514699911	43	140.679	224585045044525235748388343597467245 3² × 5 × 13697 × 578131 × 2052317 × 11533673 × 26625914303	2022-10-04	11533673	26625914303	3.351e+10	293.75	544.56

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4968559

2024609142059135603124721

80.744

203742085185980040
2³ × 3 × 5 × 7 × 32909 × 7370327309

2022-10-04

32909

7370327309

89,606

80.713

150.74

4968559

2231728093642762521609553280152576514699911

140.679

224585045044525235748388343597467245
3² × 5 × 13697 × 578131 × 2052317 × 11533673 × 26625914303

2022-10-04

11533673

26625914303

3.351e+10

293.75

544.56

exponent	prime factors	composite factor	digits	bits*
4968559	2024609142059135603124721 2231728093642762521609553280152576514699911	45183771009793436702136227134013940147560528360406 89096521220599831	67	221.423

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-09-17	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	0.571%
2011-07-27	Squeeky_Squirrel	T7500_2200	60000	975000		-		-	-	0.022	-	-	0.917%
2015-04-19	mikr	MSI	1200000	43100000		-		-	-	0.700	-	-	3.980%
2022-09-19	Denial140	Manual testing	50000000	50000000		-		-	-	10.05	-	-	5.030%
2022-10-04	Denial140	i5-8400	50000000	160135168050			2024609142059135603124721 2231728093642762521609553280152576514699911	67	221.423	1,763	1.377	3,526	15.240%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.062	-	-
2009-12-14	markr	oldgamer	2⁶¹	2⁶²		-	-	0.062	-	-
2011-11-13	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.321	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.198	-	-
2014-12-29	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.395	-	-
2014-12-29	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.752	-	-
2015-07-29	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.504	-	-
2017-10-21	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	3.008	-	-
2018-06-05	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	6.016	-	-
2021-03-15	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	12.03	-	-
2021-04-23	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	24.06	-	-
2021-04-24	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	48.13	-	-
2021-04-25	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	96.26	-	-
2022-05-06	Denial140	Manual testing	2⁷²	2⁷³		-	-	192.5	-	-
2022-06-27	Denial140	Manual testing	2⁷³	2⁷⁴		-	-	385.0	-	-

ECM factoring results:

Total ECM effort:	1.894 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	1.894

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-05-20	GrunwalderGIMP	compute-0-9	50000	5000000						3	0.631
2014-04-19	S36049	Wolle5	50000	5000000						3	0.631
2017-05-28	alex	newwork	50000	5000000						3	0.631

date	userid	compid	res64	spent (GHz-days)
1998-05-16	ANONYMOUS	v4_computers	E21CAB626311547F	0.689
2000-07-03	ANONYMOUS	v4_computers	E21CAB626311547F	0.689

date

userid

compid

res64

spent (GHz-days)

1998-05-16

ANONYMOUS

v4_computers

E21CAB626311547F

0.689

2000-07-03

ANONYMOUS

v4_computers

E21CAB626311547F

0.689

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 = 50000000, B2 = 160135168050 (P-1 stage 2)

B1 = 50000000 (P-1 stage 1)

B1 = 1200000, B2 = 43100000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 60000, B2 = 975000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

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