M3345091 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	17.8186	67.6471%	1469018	111642300	1.1378	7.7634%	18.9565	70.1587%	2.5117%
PrimeNet	2⁶⁰	0.0459	63.3333%	14000	260000	0.0042	2.7852%	0.0501	64.3546%	1.0212%
GPU72	2⁶⁴	1.0640	65.6250%	18000	300000	0.0051	1.7549%	1.0691	66.2282%	0.6032%
Difference	+4	+16.7546	+2.0221%	+1451018	+111342300	+1.1328	+6.0085%	+17.8873	+3.9305%	+3.9305%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.8186

67.6471%

1469018

111642300

1.1378

7.7634%

18.9565

70.1587%

2.5117%

PrimeNet

2⁶⁰

0.0459

63.3333%

14000

260000

0.0042

2.7852%

0.0501

64.3546%

1.0212%

GPU72

2⁶⁴

1.0640

65.6250%

18000

300000

0.0051

1.7549%

1.0691

66.2282%

0.6032%

Difference

+16.7546

+2.0221%

+1451018

+111342300

+1.1328

+6.0085%

+17.8873

+3.9305%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3345091	60211639	8	25.844	9 3²	-	9	9	1.339e-12	1.371e-6	2.789e-6
3345091	10339164247920631	17	53.199	1545423465 3 × 5 × 3413 × 30187	2014-09-10	3413	30187	0.0004	0.0007	0.0011

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3345091

60211639

25.844

9
3²

1.339e-12

1.371e-6

2.789e-6

3345091

10339164247920631

53.199

1545423465
3 × 5 × 3413 × 30187

2014-09-10

3413

30187

0.0004

0.0007

0.0011

exponent	prime factors	composite factor	digits	bits*
3345091	60211639 10339164247920631	622538025257503534424209	24	79.043

exponent

prime factors

composite factor

digits

bits*

3345091

60211639
10339164247920631

622538025257503534424209

79.043

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-10T11:45:14	Jocelyn Larouche	Manual testing	334509	3679600	6	-	skipped known factor: 60211639 skipped known factor: 10339164247920631	-	-	0.079	-	-	3.518%
2021-03-10T15:34:12	Jocelyn Larouche	Manual testing	334509	7024691	6	-	skipped known factor: 60211639 skipped known factor: 10339164247920631	-	-	0.106	-	-	4.054%
2022-01-06T11:34:21	Jocelyn Larouche	Manual testing	1469018	111642300		-	skipped known factor: 60211639 skipped known factor: 10339164247920631	-	-	1.138	-	-	7.763%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-09-10T11:32:00	TJAOI	Manual testing	2⁵³	2⁵⁴*	10339164247920631	53.199	17	8.73486e-5	0.759	0.000
2022-08-10T06:25:29	LordJulius	Manual testing	2¹	2⁶²	10339164247920631	53.199	17	0.000	0.759	0.001
2022-08-10T06:25:29	LordJulius	Manual testing	2¹	2⁶²	60211639	25.844	8	1.33891e-12	0.760	2.89566e-12
2022-08-10T06:25:29	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.293	-	-
2022-08-10T06:25:29	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.587	-	-
2022-08-10T06:25:29	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.117	-	-
2022-08-10T06:25:29	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.234	-	-
2022-08-10T06:25:29	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.468	-	-
2021-10-20T10:52:33	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.936	-	-
2022-08-10T06:25:29	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	8.936	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.438 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.438 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.438

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-04T10:12:56	Niels_Mache_Nextcloud	SuperDry-T	50000	5000000						3	0.438

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T05:56:28

kkmrkkblmbrbk

old

60211639

10339164247920631

A757A71DA97837__

2017-11-20T08:27:13

Oliver Kruse

Threadripper

60211639

10339164247920631

A757A71DA97837__

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 = 1469018, B2 = 111642300 (P-1 stage 2)

B1 = 1469018 (P-1 stage 1)

B1 = 334509, B2 = 7024691 (P-1 stage 2)

B1 = 334509, B2 = 3679600 (P-1 stage 2)

B1 = 334509 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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