M2175559 Mersenne number exponent details

Residue

Status

L-L

BD8F7DCD27798FA4

double-checked

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	13.6581	67.1642%	500000	15000000	0.1230	5.1751%	13.7810	68.8635%	1.6993%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8572%	0.0195	63.1527%	1.0838%
GPU72	2⁶²	0.2824	64.5161%	11000	160000	0.0018	1.5681%	0.2842	65.0726%	0.5564%
Difference	+5	+13.3757	+2.6481%	+489000	+14840000	+0.1212	+3.6070%	+13.4968	+3.7909%	+3.7909%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.6581

67.1642%

500000

15000000

0.1230

5.1751%

13.7810

68.8635%

1.6993%

PrimeNet

2⁵⁸

0.0176

62.0690%

10000

180000

0.0018

2.8572%

0.0195

63.1527%

1.0838%

GPU72

2⁶²

0.2824

64.5161%

11000

160000

0.0018

1.5681%

0.2842

65.0726%

0.5564%

Difference

+13.3757

+2.6481%

+489000

+14840000

+0.1212

+3.6070%

+13.4968

+3.7909%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2175559	194495125079064913	18	57.433	44700034584 2³ × 3 × 43 × 569 × 76123	1999-01-29	569	76123	0.0102	0.0004	0.0007

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2175559

194495125079064913

57.433

44700034584
2³ × 3 × 43 × 569 × 76123

1999-01-29

569

76123

0.0102

0.0004

0.0007

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T13:46:03	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 194495125079064913	-	-	0.123	-	-	5.175%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	?	?	194495125079064913	57.433	18	0.001	0.291	0.003
2000-04-05T00:00:00	ANONYMOUS	v4_computers	?	?	194495125079064913	57.433	18	0.001	0.291	0.003
2002-09-07T00:00:00	ANONYMOUS	v4_computers	?	?	194495125079064913	57.433	18	0.001	0.291	0.003

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.138 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.138 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.946	38.848%
25	50000	0.087	91.629%
30	250000	0.006	99.448%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		17	1.453
50000	6750000		7	0.684

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-14T15:20:29	Michel Thull	MT-Thinkpad	50000	5000000						3	0.256
2022-03-06T18:43:56	Dylan Delgado	colab	50000	6750000						7	0.684
2022-06-10T15:16:38	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.598
2022-08-08T05:56:21	MarkS	laptop64	50000	5000000						7	0.598

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T16:15:41

kkmrkkblmbrbk

old

194495125079064913

88EE2DF74DC34E__

2017-10-22T23:50:57

Oliver Kruse

GTX-1

194495125079064913

88EE2DF74DC34E__

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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