M31663 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	200000000	5000000000	0.3686	48.9227%	0.3686	48.9227%	48.9227%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1603%	0.0000	64.0601%	1.5601%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7867%	0.0001	66.5182%	0.6091%
Difference	-44	-0.0001	-65.9091%	+199999500	+4999990000	+0.3686	+47.1361%	+0.3685	-17.5955%	-17.5955%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

200000000

5000000000

0.3686

48.9227%

0.3686

48.9227%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1603%

0.0000

64.0601%

1.5601%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7867%

0.0001

66.5182%

0.6091%

Difference

-44

-0.0001

-65.9091%

+199999500

+4999990000

+0.3686

+47.1361%

+0.3685

-17.5955%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31663	2935382553345929	16	51.382	46353512828 2² × 7 × 37 × 44742773	2014-04-23	37	44742773	0.0179	0.0019	0.0036
31663	34654119353633114722489	23	74.875	547233669482252388 2² × 3 × 29 × 1163 × 1352115687437	2010-04-20	1163	1352115687437	209,967	58.838	109.89
31663	423578061881736532997879	24	78.487	6688849159614321653 19 × 352044692611280087	2015-07-03	19	352044692611280087	2,558,169	15,319,518	28,612,594
31663	58640126552592125788807705469119	32	105.532	926003956551686918308557393 3 × 53 × 167703727 × 34727458710813601	2017-08-15	167703727	34727458710813601	4.227e+12	1,511,194	2,822,490

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31663

2935382553345929

51.382

46353512828
2² × 7 × 37 × 44742773

2014-04-23

44742773

0.0179

0.0019

0.0036

31663

34654119353633114722489

74.875

547233669482252388
2² × 3 × 29 × 1163 × 1352115687437

2010-04-20

1163

1352115687437

209,967

58.838

109.89

31663

423578061881736532997879

78.487

6688849159614321653
19 × 352044692611280087

2015-07-03

352044692611280087

2,558,169

15,319,518

28,612,594

31663

58640126552592125788807705469119

105.532

926003956551686918308557393
3 × 53 × 167703727 × 34727458710813601

2017-08-15

167703727

34727458710813601

4.227e+12

1,511,194

2,822,490

exponent	prime factors	composite factor	digits	bits*
31663	2935382553345929 34654119353633114722489	101723097352222146973324597077252897281	39	126.258
31663	2935382553345929 423578061881736532997879	1243363652827731703673370039728510284591	40	129.869
31663	34654119353633114722489 423578061881736532997879	14678724712030291092509605856078652154310600831	47	153.362
31663	2935382553345929 58640126552592125788807705469119	172131204408476283303859142788011053626033866551	48	156.914
31663	34654119353633114722489 58640126552592125788807705469119	20321219444656778860623957008753082524302731232443 17191	55	180.407
31663	423578061881736532997879 58640126552592125788807705469119	24838671153646729046530710832173669923487064481126 998601	56	184.019
31663	2935382553345929 34654119353633114722489 423578061881736532997879	43087672425061462241371932582180659973706633483353 213377866999	62	204.745
31663	2935382553345929 34654119353633114722489 58640126552592125788807705469119	59650553020559556861925456951792651550888380834511 39390110152024565439	70	231.790
31663	2935382553345929 423578061881736532997879 58640126552592125788807705469119	72911001952711407442214433087788024026847779462048 146199522589852045329	71	235.401
31663	34654119353633114722489 423578061881736532997879 58640126552592125788807705469119	86076227474411767797096372209871317650927464976684 3224161867993650237606237889	78	258.894
31663	2935382553345929 34654119353633114722489 423578061881736532997879 58640126552592125788807705469119	25266665638622382042347972346673207114984200000474 53988410209666141113086830616383038883703881	94	310.277

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-09T01:59:41	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 2935382553345929	-	-	0.369	-	-	41.275%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-09T01:59:41

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 2935382553345929

0.369

-

-

41.275%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.206 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1373 / 100	13.730	0.000%
25	50000	1373 / 280	4.904	0.736%
30	250000	1096 / 640	1.713	18.017%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	19.206 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	159.257	0.000%
25	50000	31.980	0.000%
30	250000	5.489	0.413%
35	1000000	0.795	45.152%
40	3000000	0.098	90.635%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
		34654119353633114722489	1	0.00000e+0
50000	5000000		277	0.159
250000	25000000		445	1.279
250000	25000000	423578061881736532997879	140	0.402
1000000	100000000		11	0.126
3000000	300000000		490	16.90
3000000	300000000	58640126552592125788807705469119	10	0.345

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T14:36:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-18T01:05:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T15:28:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-20T20:08:00	James Hintz	04_122109			34654119353633114722489	74.875		1		1	-
2010-04-21T00:01:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T04:00:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T11:05:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-21T11:59:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-26T14:54:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-26T18:47:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-26T22:46:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T02:45:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T06:44:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T11:23:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T18:38:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-27T22:37:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T02:36:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T10:30:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T14:20:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T18:31:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-28T22:19:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-04-29T02:31:00	James Hintz	04_122109	50000	5000000						11	0.006
2010-05-10T09:16:00	James Hintz	04_122109	50000	5000000						27	0.016
2011-01-20T22:03:00	James Hintz	NEW_OMFG	250000	25000000						4	0.011
2011-03-16T17:25:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-06-23T17:25:00	James Hintz	08_04_2014	250000	25000000						11	0.032
2015-07-03T09:23:00	James Hintz	08_04_2014	250000	25000000	423578061881736532997879	78.487	140	2		140	0.402
2015-07-03T13:49:00	James Hintz	08_04_2014	250000	25000000						419	1.204
2015-07-03T14:18:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-08-15T19:58:53	nordi	nordiputer	3000000	300000000	58640126552592125788807705469119	105.532	10	2		10	0.345
2017-08-18T17:46:14	nordi	nordiputer	3000000	300000000						490	16.90

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