M3277097 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	18.1883	67.6471%	1000000	134343300	1.2587	7.6495%	19.4470	70.1219%	2.4749%
PrimeNet	2⁶⁰	0.0469	63.3333%	14000	260000	0.0042	2.7750%	0.0510	64.3508%	1.0175%
GPU72	2⁶⁴	1.0861	65.6250%	17000	280000	0.0048	1.6870%	1.0909	66.2049%	0.5799%
Difference	+4	+17.1022	+2.0221%	+983000	+134063300	+1.2539	+5.9625%	+18.3561	+3.9170%	+3.9170%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.1883

67.6471%

1000000

134343300

1.2587

7.6495%

19.4470

70.1219%

2.4749%

PrimeNet

2⁶⁰

0.0469

63.3333%

14000

260000

0.0042

2.7750%

0.0510

64.3508%

1.0175%

GPU72

2⁶⁴

1.0861

65.6250%

17000

280000

0.0048

1.6870%

1.0909

66.2049%

0.5799%

Difference

+17.1022

+2.0221%

+983000

+134063300

+1.2539

+5.9625%

+18.3561

+3.9170%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3277097	8050361306548663	16	52.838	1228276323 3² × 136475147	-	9	136475147	0.0003	1.1324	2.1149

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3277097

8050361306548663

52.838

1228276323
3² × 136475147

136475147

0.0003

1.1324

2.1149

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-25T20:19:29	Jocelyn Larouche	Manual testing	109236	109236		-		-	-	0.017	-	-	0.910%
2021-01-01T17:08:06	Jocelyn Larouche	Manual testing	327709	327709		-		-	-	0.050	-	-	1.605%
2021-01-03T02:39:38	Jocelyn Larouche	Manual testing	327709	3277097	6	-		-	-	0.074	-	-	3.405%
2022-03-13T12:30:27	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.259	-	-	7.650%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-05-21T12:00:53	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.121	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.437 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:	0.437 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	0.437

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-09-25T10:33:35	Niels_Mache_Nextcloud	SuperDry-T	50000	5000000						3	0.437

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-03T07:01:15

Oliver Kruse

GTX-0

8050361306548663

EE8676A6EC5AA0__

2017-12-14T05:47:12

kkmrkkblmbrbk

c4.xlarge

8050361306548663

EE8676A6EC5AA0__

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 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 327709, B2 = 3277097 (P-1 stage 2)

B1 = 327709 (P-1 stage 1)

B1 = 109236 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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