M1835027 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	16.1926	68.6567%	500000	15000000	0.1015	5.0703%	16.2941	70.2459%	1.5892%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8806%	0.0117	64.2192%	1.0613%
GPU72	2⁶¹	0.1674	65.5738%	9000	140000	0.0013	1.5955%	0.1687	66.1230%	0.5493%
Difference	+6	+16.0252	+3.0829%	+491000	+14860000	+0.1002	+3.4748%	+16.1254	+4.1229%	+4.1229%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1926

68.6567%

500000

15000000

0.1015

5.0703%

16.2941

70.2459%

1.5892%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8806%

0.0117

64.2192%

1.0613%

GPU72

2⁶¹

0.1674

65.5738%

9000

140000

0.0013

1.5955%

0.1687

66.1230%

0.5493%

Difference

+16.0252

+3.0829%

+491000

+14860000

+0.1002

+3.4748%

+16.1254

+4.1229%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1835027	5272194053377	13	42.262	1436544 2⁷ × 3² × 29 × 43	-	128	128	6.195e-7	1.007e-5	2.049e-5
1835027	164622786156991	15	47.226	44855685 3² × 5 × 7 × 157 × 907	2008-08-26	157	907	1.045e-5	1.556e-5	2.513e-5
1835027	4577049121661501351256367063	28	91.886	1247133999026036497353 3 × 1291 × 322007229286350761	2020-09-08	1291	322007229286350761	399,458,863	1.380e+9	2.578e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1835027

5272194053377

42.262

1436544
2⁷ × 3² × 29 × 43

128

6.195e-7

1.007e-5

2.049e-5

1835027

164622786156991

47.226

44855685
3² × 5 × 7 × 157 × 907

2008-08-26

157

907

1.045e-5

1.556e-5

2.513e-5

1835027

4577049121661501351256367063

91.886

1247133999026036497353
3 × 1291 × 322007229286350761

2020-09-08

1291

322007229286350761

399,458,863

1.380e+9

2.578e+9

exponent	prime factors	composite factor	digits	bits*
1835027	5272194053377 164622786156991	867923274227241464955708607	27	89.488
1835027	5272194053377 4577049121661501351256367063	24131091161238188422011668517357326721751	41	134.148
1835027	164622786156991 4577049121661501351256367063	753486578785324820045348504784785839587433	42	139.113
1835027	5272194053377 164622786156991 4577049121661501351256367063	39725274599713699201184490343958863346553404976604 11241	55	181.374

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:40:01	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 5272194053377 skipped known factor: 164622786156991	-	-	0.101	-	-	5.070%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:40:01

alpertron

Manual testing

500000

15000000

skipped known factor: 5272194053377
skipped known factor: 164622786156991

0.101

-

-

5.070%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	164622786156991	47.226	15	2.32209e-7	0.213	4.96569e-7

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

164622786156991

47.226

2.32209e-7

0.213

4.96569e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.346 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	20.346 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	9.065	0.012%
25	50000	0.821	43.990%
30	250000	0.051	95.046%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.004
50000	5000000	4577049121661501351256367063	4	0.276
50000	6534230		14	1.085
50000	6600000		218	16.98

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T01:41:23	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-01-02T04:33:55	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-13T17:33:14	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-20T18:35:28	nordi	sweet16	50000	5000000						3	0.207
2020-07-18T01:14:30	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-09-08T22:50:34	Chang Chia-Tche	exbpc13	50000	5000000	4577049121661501351256367063	91.886	4	2		4	0.276
2020-10-30T23:52:12	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-01-18T10:28:46	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-05-07T10:27:44	TJAOI	Manual testing	50000	6600000						218	16.98
2021-06-22T19:26:03	seatsea	dt	50000	6534230						7	0.543
2021-07-14T09:06:11	seatsea	Manual testing	50000	6534230						7	0.543

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T02:40:38

Oliver Kruse

GTX-2

5272194053377

164622786156991

7979FA85A2514E__

2017-11-06T10:13:25

kkmrkkblmbrbk

c4.xlarge

5272194053377

164622786156991

7979FA85A2514E__

2020-09-09T00:59:36

CrypticClue

cruncher

5272194053377

164622786156991

4577049121661501351256367063

B9C382258049E840

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

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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