M2273549 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	2⁶⁷	13.0694	67.1642%	500000	15000000	0.1230	5.2025%	13.1924	68.8725%	1.7083%
PrimeNet	2⁵⁸	0.0169	62.0690%	10000	190000	0.0019	2.9218%	0.0188	63.1772%	1.1083%
GPU72	2⁶²	0.2702	64.5161%	12000	190000	0.0021	1.7083%	0.2723	65.1223%	0.6062%
Difference	+5	+12.7992	+2.6481%	+488000	+14810000	+0.1209	+3.4943%	+12.9201	+3.7502%	+3.7502%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.0694

67.1642%

500000

15000000

0.1230

5.2025%

13.1924

68.8725%

1.7083%

PrimeNet

2⁵⁸

0.0169

62.0690%

10000

190000

0.0019

2.9218%

0.0188

63.1772%

1.1083%

GPU72

2⁶²

0.2702

64.5161%

12000

190000

0.0021

1.7083%

0.2723

65.1223%

0.6062%

Difference

+12.7992

+2.6481%

+488000

+14810000

+0.1209

+3.4943%

+12.9201

+3.7502%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2273549	5694155557507591	16	52.338	1252261455 3 × 5 × 659 × 126683	-	659	126683	0.0003	0.0007	0.0012
2273549	86962330536731904937	20	66.237	19124797956132 2² × 3 × 11 × 144884833001	2018-01-26	11	144884833001	7.6227	752.57	1,405.6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2273549

5694155557507591

52.338

1252261455
3 × 5 × 659 × 126683

659

126683

0.0003

0.0007

0.0012

2273549

86962330536731904937

66.237

19124797956132
2² × 3 × 11 × 144884833001

2018-01-26

144884833001

7.6227

752.57

1,405.6

exponent	prime factors	composite factor	digits	bits*
2273549	5694155557507591 86962330536731904937	495177037719544065435684569267876767	36	118.575

exponent

prime factors

composite factor

digits

bits*

2273549

5694155557507591
86962330536731904937

495177037719544065435684569267876767

118.575

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-04-30T16:59:32	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 5694155557507591	-	-	0.123	-	-	5.203%

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.985 GHz-days
Estimated T-Level:	0.550

Digits	B1	Curves	Complete	FacMiss
20	11000	11 / 100	0.110	89.534%
25	50000	11 / 280	0.039	96.141%

New Calculation Method

Total ECM effort:	0.985 GHz-days
Estimated T-Level:	0.550

Digits	B1	Complete	FacMiss
20	11000	0.434	64.801%
25	50000	0.040	96.073%
30	250000	0.003	99.747%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.258
50000	5000000	86962330536731904937	1	0.086
50000	5795104		7	0.642

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-26T17:18:22	ATH	ec2-1xe	50000	5000000	86962330536731904937	66.237	1	2		1	0.086
2018-09-16T21:26:19	Ra1nb0w	ra1nb0w_H	50000	5000000						3	0.258
2022-08-07T06:43:24	debrouxl	z400	50000	5795104						7	0.642

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-11T03:00:20

Oliver Kruse

GTX-0

5694155557507591

1EA3D216FB064C__

2017-11-21T23:38:41

kkmrkkblmbrbk

c4.xlarge

5694155557507591

1EA3D216FB064C__

2018-01-27T16:04:23

trebor

Laptop

5694155557507591

86962330536731904937

3E659C14A84D5D__

2018-01-29T03:49:17

Oliver Kruse

GTX-2

5694155557507591

86962330536731904937

3E659C14A84D5D__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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