M10203883 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

0EFA28E41FD82A__

unverified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	11.7001	65.2174%	2000000	40000000	1.9280	6.9814%	13.6281	67.6457%	2.4283%
PrimeNet	2⁶⁴	0.3488	62.5000%	45000	1300000	0.0537	3.7559%	0.4025	63.9085%	1.4085%
GPU72	2⁶⁸	5.8414	64.7059%	70000	1600000	0.0726	2.6552%	5.9140	65.6430%	0.9371%
Difference	+1	+5.8587	+0.5115%	+1930000	+38400000	+1.8553	+4.3262%	+7.7141	+2.0027%	+2.0027%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

11.7001

65.2174%

2000000

40000000

1.9280

6.9814%

13.6281

67.6457%

2.4283%

PrimeNet

2⁶⁴

0.3488

62.5000%

45000

1300000

0.0537

3.7559%

0.4025

63.9085%

1.4085%

GPU72

2⁶⁸

5.8414

64.7059%

70000

1600000

0.0726

2.6552%

5.9140

65.6430%

0.9371%

Difference

+5.8587

+0.5115%

+1930000

+38400000

+1.8553

+4.3262%

+7.7141

+2.0027%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10203883	102038831	9	26.605	5 5	-	1	5	8.771e-13	5.769e-7	9.640e-7
10203883	31774891663	11	34.887	1557 3² × 173	2008-09-08	9	173	2.999e-10	8.495e-6	8.676e-6
10203883	1562765496983	13	40.507	76577 73 × 1049	2008-09-08	73	1049	2.261e-8	5.976e-5	7.037e-5
10203883	28328917737266863543	20	64.619	1388143990737 3² × 7 × 13669 × 1611971	2017-11-22	13669	1611971	0.4437	0.0477	0.0777
10203883	178141276689751370993	21	67.272	8729092478312 2³ × 17 × 353 × 2069 × 87881	2022-01-22	2069	87881	3.9214	0.0032	0.0042

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

10203883

102038831

26.605

5
5

8.771e-13

5.769e-7

9.640e-7

10203883

31774891663

34.887

1557
3² × 173

2008-09-08

173

2.999e-10

8.495e-6

8.676e-6

10203883

1562765496983

40.507

76577
73 × 1049

2008-09-08

1049

2.261e-8

5.976e-5

7.037e-5

10203883

28328917737266863543

64.619

1388143990737
3² × 7 × 13669 × 1611971

2017-11-22

13669

1611971

0.4437

0.0477

0.0777

10203883

178141276689751370993

67.272

8729092478312
2³ × 17 × 353 × 2069 × 87881

2022-01-22

2069

87881

3.9214

0.0032

0.0042

exponent	prime factors	composite factor	digits	bits*
10203883	102038831 31774891663	3242272800444165953	19	61.492
10203883	102038831 1562765496983	159462764439279346873	21	67.112
10203883	31774891663 1562765496983	49656704361309178352729	23	75.394
10203883	102038831 28328917737266863543	2890649649405875890964238233	28	91.223
10203883	102038831 178141276689751370993	18177327626269779576773029183	29	93.876
10203883	31774891663 28328917737266863543	900148292031693686798629342009	30	99.506
10203883	102038831 31774891663 1562765496983	5066912064340590188682972819799	31	101.999
10203883	31774891663 178141276689751370993	5660419767525357075708295731359	31	102.159
10203883	1562765496983 28328917737266863543	44271455206670373824874039190769	32	105.126
10203883	1562765496983 178141276689751370993	278393040799245414392581255214119	33	107.779
10203883	102038831 31774891663 28328917737266863543	91850079445560638751012270460897551479	38	126.111
10203883	102038831 31774891663 178141276689751370993	577582616047579198862852993430162401329	39	128.763
10203883	102038831 1562765496983 28328917737266863543	4517407535957508347423145681274254751039	40	131.731
10203883	28328917737266863543 178141276689751370993	5046549572955661672095635365493299408199	40	131.890
10203883	102038831 1562765496983 178141276689751370993	28406900441690307766729566354561357454889	41	134.383
10203883	31774891663 1562765496983 28328917737266863543	1406720692955308403237083529907901164658847	43	140.013
10203883	31774891663 1562765496983 178141276689751370993	8845908711129161974473810335353185092989897	43	142.666
10203883	102038831 28328917737266863543 178141276689751370993	514944019007944931852143952897194009945617775369	48	158.495
10203883	102038831 31774891663 1562765496983 28328917737266863543	14354013505266960471078861924115577250532726168785 7	51	166.618
10203883	31774891663 28328917737266863543 178141276689751370993	16035356595262506433332024391370099724794523894493 7	51	166.778
10203883	102038831 31774891663 1562765496983 178141276689751370993	90262618401633637788495944673515697901531538469040 7	51	169.271
10203883	1562765496983 28328917737266863543 178141276689751370993	78865735514294010292161403850602868986105300199636 17	52	172.398
10203883	102038831 31774891663 28328917737266863543 178141276689751370993	16362290416487262945871792037588914642714549333957 044848647	59	193.382
10203883	102038831 1562765496983 28328917737266863543 178141276689751370993	80473674578337446005141181122344153965883400752749 4141211727	60	199.002
10203883	31774891663 1562765496983 28328917737266863543 178141276689751370993	25059502018895037649632355854628971992704785661535 3157376625071	63	207.285
10203883	102038831 31774891663 1562765496983 28328917737266863543 178141276689751370993	25570422914501895534694731711823462408673368570086 252830869848970132001	71	233.889

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-01-28T20:16:28	riccardo uberti	Colab_noGPU14	2000000	40000000		-	skipped known factor: 102038831 skipped known factor: 31774891663 skipped known factor: 1562765496983 skipped known factor: 28328917737266863543 skipped known factor: 178141276689751370993	-	-	1.928	-	-	6.981%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-01-28T20:16:28

riccardo uberti

Colab_noGPU14

2000000

40000000

skipped known factor: 102038831
skipped known factor: 31774891663
skipped known factor: 1562765496983
skipped known factor: 28328917737266863543
skipped known factor: 178141276689751370993

1.928

-

-

6.981%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T06:27:00	Will Edgington	Manual testing	?	?	1562765496983	40.507	13	8.25558e-9	7.123	1.76411e-8
2008-09-08T06:27:00	Will Edgington	Manual testing	?	?	31774891663	34.887	11	7.55901e-11	7.123	1.61526e-10
2017-11-22T12:46:14	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	28328917737266863543	64.619	20	0.095	6.774	0.193
2022-03-22T17:30:14	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.732	-	-
2022-03-22T17:30:14	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	1.465	-	-
2022-01-22T13:07:56	ViliamF	Manual testing	2⁶⁷	2⁶⁸	178141276689751370993	67.272	21	1.009	6.774	2.051
2022-01-22T13:07:57	ViliamF	Manual testing	2⁶⁷	2⁶⁸	skipped known factors(?)	-	-	2.929	-	-
2022-01-22T13:07:57	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	5.859	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.614 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	9.614 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.435	64.741%
25	50000	0.040	96.125%
30	250000	0.003	99.748%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	14400000		10	9.61

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