M15527 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	unknown	10000000	4626851679450	87.1192	63.8010%	87.1192	63.8010%	63.8010%
PrimeNet	2⁴⁰	0.0000	65.0000%	500	10000	0.0000	3.4590%	0.0000	66.2106%	1.2106%
GPU72	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.4451%	0.0002	68.6416%	0.4598%
Difference	-44	-0.0002	-68.1818%	+9999500	+4626851669450	+87.1192	+62.3559%	+87.1190	-4.8406%	-4.8406%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

10000000

4626851679450

87.1192

63.8010%

87.1192

63.8010%

PrimeNet

2⁴⁰

0.0000

65.0000%

500

10000

0.0000

3.4590%

0.0000

66.2106%

1.2106%

GPU72

2⁴⁴

0.0002

68.1818%

500

10000

0.0000

1.4451%

0.0002

68.6416%

0.4598%

Difference

-44

-0.0002

-68.1818%

+9999500

+4626851669450

+87.1192

+62.3559%

+87.1190

-4.8406%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15527	457610253409	12	38.735	14735952 2⁴ × 3³ × 7 × 11 × 443	-	27	443	3.773e-6	1.716e-8	1.899e-8
15527	6761941358632326545009	22	72.518	217747837915641352 2³ × 11 × 6359 × 87803 × 4431727	2008-08-29	87803	4431727	75,086	0.0001	0.0002
15527	93102780834842463427951219061039959063	38	126.130	2998093026175129240289534973305853 3³ × 101 × 2508740581 × 438232125578211647519	2021-12-10	2508740581	438232125578211647519	1.012e+13	8.251e+9	1.541e+10

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15527

457610253409

38.735

14735952
2⁴ × 3³ × 7 × 11 × 443

443

3.773e-6

1.716e-8

1.899e-8

15527

6761941358632326545009

72.518

217747837915641352
2³ × 11 × 6359 × 87803 × 4431727

2008-08-29

87803

4431727

75,086

0.0001

0.0002

15527

93102780834842463427951219061039959063

126.130

2998093026175129240289534973305853
3³ × 101 × 2508740581 × 438232125578211647519

2021-12-10

2508740581

438232125578211647519

1.012e+13

8.251e+9

1.541e+10

exponent	prime factors	composite factor	digits	bits*
15527	457610253409 6761941358632326545009	3094333698660536699920805934185681	34	111.253
15527	457610253409 93102780834842463427951219061039959063	42604787130914848265858572168212966705894416195767	50	164.865
15527	6761941358632326545009 93102780834842463427951219061039959063	62955554433080238060409187692156285862698372994679 7586966567	60	198.648
15527	457610253409 6761941358632326545009 93102780834842463427951219061039959063	28809107217625941071253895030039481855261646646627 4065859800440480776903	72	237.383

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-06T16:46:52	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 457610253409	-	-	1.72792e-5	-	-	6.340%
2022-04-11T00:31:48	Ethan O'Connor	Manual testing	10000000	4626851679450		-	skipped known factor: 457610253409 skipped known factor: 6761941358632326545009	-	-	87.12	-	-	53.969%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-02-06T16:46:52

Lisander Viaene

Manual testing

50000

skipped known factor: 457610253409

1.72792e-5

-

-

6.340%

2022-04-11T00:31:48

Ethan O'Connor

Manual testing

10000000

4626851679450

skipped known factor: 457610253409
skipped known factor: 6761941358632326545009

87.12

-

-

53.969%

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.241 GHz-days
Estimated T-Level:	35.957

Digits	B1	Curves	Complete	FacMiss
20	11000	3116 / 100	31.160	0.000%
25	50000	3116 / 280	11.129	0.001%
30	250000	2968 / 640	4.638	0.965%
35	1000000	2296 / 1580	1.453	23.372%
40	3000000	900 / 4700	0.191	82.571%

New Calculation Method

Total ECM effort:	21.241 GHz-days
Estimated T-Level:	35.957

Digits	B1	Complete	FacMiss
20	11000	440.203	0.000%
25	50000	91.271	0.000%
30	250000	15.438	0.000%
35	1000000	2.136	11.809%
40	3000000	0.249	77.982%
45	11000000	0.025	97.504%
50	44000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
		6761941358632326545009	1	0.00000e+0
50000	5000000		148	0.037
250000	25000000		672	0.835
1000000	100000000		1,396	6.942
3000000	300000000		396	5.908
3000000	300000000	93102780834842463427951219061039959063	504	7.519

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29T02:24:00	ANONYMOUS	Manual testing			6761941358632326545009	72.518		1		1	-
2009-04-07T19:18:00	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.012
2009-06-08T19:54:00	unconnected	dual5430	250000	25000000						30	0.037
2009-06-12T04:05:00	Rob_Dee	twopc	50000	5000000						80	0.020
2009-07-04T21:16:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05T02:35:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05T10:34:00	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05T15:42:00	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-06T07:47:00	Rob_Dee	twopc	250000	25000000						10	0.012
2010-04-07T20:38:00	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-09T01:50:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-09T11:44:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-09T21:51:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-10T07:50:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-10T18:19:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-11T04:14:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-11T15:25:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-12T01:00:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-12T18:02:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-12T23:06:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-13T09:16:00	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-22T06:12:00	Bud	annan	250000	25000000						500	0.622
2010-04-26T07:06:00	Bud	annan	1000000	100000000						100	0.497
2011-04-07T14:47:00	James Hintz	17_051310	1000000	100000000						11	0.055
2017-10-17T18:07:21	James Hintz	10_12_2017	1000000	100000000						1285	6.390
2019-01-24T21:25:23	Dylan Delgado	laptop-i55200	3000000	300000000						250	3.730
2021-12-10T10:44:40	nordi	sweet16_ccx1	3000000	300000000	93102780834842463427951219061039959063	126.130	504	2	5563546201078335	504	7.519
2021-12-10T19:00:55	nordi	sweet16_ccx2	3000000	300000000						146	2.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:15:22

Oliver Kruse

PRP

457610253409

6761941358632326545009

9B558421B8EFDB__

2017-09-21T21:28:31

Oliver Kruse

Manual testing

457610253409

6761941358632326545009

9B558421B8EFDB__

2017-10-12T16:01:22

kkmrkkblmbrbk

Manual testing

457610253409

6761941358632326545009

9B558421B8EFDB__

2020-04-17T13:48:11

Oliver Kruse

Manual testing

457610253409

6761941358632326545009

FB50DE0076F70B__

2021-12-10T10:44:41

nordi

sweet16_ccx1

457610253409

6761941358632326545009

93102780834842463427951219061039959063

FB50DE0076F70B54

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