M556103 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	53.4324	70.1493%	1500000	50000000	0.0876	6.1703%	53.5200	71.9911%	1.8419%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	190000	0.0003	19.7966%	0.0003	59.8983%	9.8983%
GPU72	2⁴⁴	0.0000	54.5455%	10000	320000	0.0006	15.0052%	0.0006	61.3660%	6.8206%
Difference	+23	+53.4324	+15.6038%	+1490000	+49680000	+0.0870	-8.8349%	+53.5194	+10.6251%	+10.6251%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

53.4324

70.1493%

1500000

50000000

0.0876

6.1703%

53.5200

71.9911%

1.8419%

PrimeNet

2⁴⁰

0.0000

50.0000%

5500

190000

0.0003

19.7966%

0.0003

59.8983%

9.8983%

GPU72

2⁴⁴

0.0000

54.5455%

10000

320000

0.0006

15.0052%

0.0006

61.3660%

6.8206%

Difference

+23

+53.4324

+15.6038%

+1490000

+49680000

+0.0870

-8.8349%

+53.5194

+10.6251%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
556103	7926906817759	13	42.850	7127193 3 × 71 × 33461	-	71	33461	1.773e-6	3.997e-5	7.200e-5
556103	273788058496081	15	47.960	246166680 2³ × 3 × 5 × 499 × 4111	2008-09-30	499	4111	6.174e-5	1.471e-5	2.147e-5
556103	116422130217581285835352183	27	86.589	104676768707938354797 3 × 83401 × 418367360534999	2020-09-04	83401	418367360534999	29,260,535	481,994	900,231

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

556103

7926906817759

42.850

7127193
3 × 71 × 33461

33461

1.773e-6

3.997e-5

7.200e-5

556103

273788058496081

47.960

246166680
2³ × 3 × 5 × 499 × 4111

2008-09-30

499

4111

6.174e-5

1.471e-5

2.147e-5

556103

116422130217581285835352183

86.589

104676768707938354797
3 × 83401 × 418367360534999

2020-09-04

83401

418367360534999

29,260,535

481,994

900,231

exponent	prime factors	composite factor	digits	bits*
556103	7926906817759 273788058496081	2170292427513584383082702479	28	90.810
556103	7926906817759 116422130217581285835352183	922867377759771184775022954967563817897	39	129.439
556103	273788058496081 116422130217581285835352183	31874988998249504486471923788117960294823	41	134.550
556103	7926906817759 273788058496081 116422130217581285835352183	25267006760621711483035775086036891321634930037216 1657	54	177.399

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T18:48:43	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 7926906817759 skipped known factor: 273788058496081	-	-	0.088	-	-	6.170%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-30T13:18:00	markr	Manual testing	?	?	273788058496081	47.960	15	2.80225e-5	0.017	5.85273e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-09-30T13:18:00

markr

Manual testing

273788058496081

47.960

2.80225e-5

0.017

5.85273e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	24.350 GHz-days
Estimated T-Level:	26.914

Digits	B1	Curves	Complete	FacMiss
20	11000	526 / 100	5.260	0.506%
25	50000	526 / 280	1.879	15.230%
30	250000	245 / 640	0.383	68.174%

New Calculation Method

Total ECM effort:	24.350 GHz-days
Estimated T-Level:	26.914

Digits	B1	Complete	FacMiss
20	11000	29.481	0.000%
25	50000	3.771	2.303%
30	250000	0.369	69.139%
35	1000000	0.029	97.159%
40	3000000	0.002	99.814%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	4.543
250000	25000000		144	11.64
250000	25000000	116422130217581285835352183	101	8.165

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-25T15:21:00	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-07-31T09:48:00	TJAOI	Manual testing	50000	5000000						99	1.601
2016-03-18T10:47:03	TJAOI	Manual testing	50000	5000000						90	1.455
2016-07-22T12:42:50	TJAOI	Manual testing	50000	5000000						91	1.471
2018-08-17T13:22:19	TJAOI	Manual testing	250000	25000000						44	3.557
2020-09-04T02:38:34	nordi	sweet16	250000	25000000	116422130217581285835352183	86.589	101	2	3613614027070557	101	8.165
2021-02-12T10:25:20	TJAOI	Manual testing	250000	25000000						100	8.084

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T10:54:57

Oliver Kruse

GTX-3

7926906817759

273788058496081

2DB8C0C2105CE2__

2017-09-28T09:43:12

Oliver Kruse

Manual testing

7926906817759

273788058496081

2DB8C0C2105CE2__

2017-11-09T05:36:04

kkmrkkblmbrbk

c4.large

7926906817759

273788058496081

2DB8C0C2105CE2__

2020-04-19T06:33:33

Oliver Kruse

AddPrpType5

7926906817759

273788058496081

94D805DACA4205__

2020-09-04T02:59:21

ATH

ec2-PRPCF

7926906817759

273788058496081

116422130217581285835352183

94D805DACA420580

2020-09-04T15:31:04

atrench

Thinkpad

7926906817759

273788058496081

116422130217581285835352183

94D805DACA420580

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 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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