M28163 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	unknown	500000000	10000000000	0.8128	50.1392%	0.8128	50.1392%	50.1392%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0378%	0.0000	64.0142%	1.5142%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7262%	0.0001	66.4976%	0.5885%
Difference	-44	-0.0001	-65.9091%	+499999500	+9999990000	+0.8128	+48.4130%	+0.8127	-16.3584%	-16.3584%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28163	8843183	7	23.076	157 157	-	1	157	4.103e-11	7.587e-9	1.287e-8
28163	440778910513165128769	21	68.579	7825496405091168 2⁵ × 3 × 81515587553033	2008-08-29	32	81515587553033	2,910.4	3,547.2	6,625.2
28163	19140090954603209561561	23	74.019	339809163700657060 2² × 5 × 167 × 3907 × 26040253537	2010-04-18	3907	26040253537	170,546	1.1332	2.1164
28163	79032332181916369547027482257443977	35	115.928	1403123463088384929642216423276 2² × 3 × 11 × 613 × 182549 × 94990904497679416739	2018-03-06	182549	94990904497679416739	4.754e+12	4.134e+9	7.720e+9

exponent	prime factors	composite factor	digits	bits*
28163	8843183 440778910513165128769	3897888568208543142922831727	28	91.655
28163	8843183 19140090954603209561561	169259326948200874540233688663	30	97.095
28163	8843183 79032332181916369547027482257443977	698897376401475746599991131631830200858791	42	139.004
28163	440778910513165128769 19140090954603209561561	8436548438092889432415763646469142597648409	43	142.598
28163	8843183 440778910513165128769 19140090954603209561561	74605941726419592249618730010473931844100250445847	50	165.674
28163	440778910513165128769 79032332181916369547027482257443977	34835785274459656001143463881269843701948171266008 474313	56	184.507
28163	19140090954603209561561 79032332181916369547027482257443977	15126860263162936455961788745123302630828145458946 90168097	58	189.947
28163	8843183 440778910513165128769 79032332181916369547027482257443977	30805922413075196413515986035595950023772513502065 4617900658279	63	207.583
28163	8843183 19140090954603209561561 79032332181916369547027482257443977	13376959352257800589744153888046572272879473184408 643884782532751	65	213.023
28163	440778910513165128769 19140090954603209561561 79032332181916369547027482257443977	66676009862818494782747777583775129683513368680475 4680436507374694855260682593	78	258.526
28163	8843183 440778910513165128769 19140090954603209561561 79032332181916369547027482257443977	58962815692670884514838384001662130264004080218791 30909206554595276174228728874813519	85	281.602

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-12-28T07:28:37	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 8843183	-	-	0.813	-	-	42.812%

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	1280 / 100	12.800	0.000%
25	50000	1280 / 280	4.571	1.026%
30	250000	1119 / 640	1.748	17.381%
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	157.432	0.000%
25	50000	31.918	0.000%
30	250000	5.498	0.409%
35	1000000	0.797	45.082%
40	3000000	0.098	90.623%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
		440778910513165128769	1	0.00000e+0
		19140090954603209561561	1	0.00000e+0
50000	5000000		161	0.093
250000	25000000		608	1.747
1000000	100000000		11	0.126
3000000	300000000		440	15.17
3000000	300000000	79032332181916369547027482257443977	60	2.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29T02:24:00	ANONYMOUS	Manual testing			440778910513165128769	68.579		1		1	-
2009-04-04T14:31:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2009-05-10T17:33:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2010-04-18T20:58:00	James Hintz	10_122109			19140090954603209561561	74.019		1		1	-
2010-04-19T11:11:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T06:45:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T02:16:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T21:36:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-22T19:14:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23T11:15:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24T06:58:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24T19:20:00	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-25T02:19:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25T22:24:00	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-20T05:49:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-18T09:08:00	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-18T09:35:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-03-06T01:06:49	nordi	nordiputer	3000000	300000000	79032332181916369547027482257443977	115.928	60	2		60	2.069
2018-03-10T01:58:25	nordi	nordiputer	3000000	300000000						440	15.17

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:37:58

Oliver Kruse

Oliver-PC

8843183

440778910513165128769

19140090954603209561561

71945A3D11E85AEA

2017-09-21T20:27:17

Oliver Kruse

Manual testing

8843183

440778910513165128769

19140090954603209561561

71945A3D11E85AEA

2017-10-02T10:28:52

kkmrkkblmbrbk

Manual testing

8843183

440778910513165128769

19140090954603209561561

71945A3D11E85A__

2017-12-07T03:12:01

ATH

xps

8843183

440778910513165128769

19140090954603209561561

71945A3D11E85A__

2018-03-06T01:11:09

ATH

ec2-1xd

8843183

440778910513165128769

19140090954603209561561

79032332181916369547027482257443977

39D3A15EF45068__

2018-03-07T19:46:50

Oliver Kruse

GTX-0

8843183

440778910513165128769

19140090954603209561561

79032332181916369547027482257443977

39D3A15EF45068__

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

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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