M1923671 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	15.4465	68.6567%	500000	15000000	0.1015	5.0991%	15.5479	70.2550%	1.5982%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0939%	0.0114	64.2978%	1.1399%
GPU72	2⁶¹	0.1597	65.5738%	10000	170000	0.0015	1.7622%	0.1612	66.1804%	0.6067%
Difference	+6	+15.2868	+3.0829%	+490000	+14830000	+0.1000	+3.3369%	+15.3868	+4.0745%	+4.0745%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4465

68.6567%

500000

15000000

0.1015

5.0991%

15.5479

70.2550%

1.5982%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0939%

0.0114

64.2978%

1.1399%

GPU72

2⁶¹

0.1597

65.5738%

10000

170000

0.0015

1.7622%

0.1612

66.1804%

0.6067%

Difference

+15.2868

+3.0829%

+490000

+14830000

+0.1000

+3.3369%

+15.3868

+4.0745%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1923671	101573676143	12	36.564	26401 17 × 1553	-	17	1553	8.159e-9	7.920e-6	1.246e-5
1923671	362419634132399279	18	58.330	94200004609 29 × 3248276021	2015-08-27	29	3248276021	0.0277	13.921	26.001
1923671	6698769752491288124089	22	72.504	1741142261980164 2² × 3 × 857 × 169305937571	2021-01-23	857	169305937571	609.50	725.60	1,355.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1923671

101573676143

36.564

26401
17 × 1553

1553

8.159e-9

7.920e-6

1.246e-5

1923671

362419634132399279

58.330

94200004609
29 × 3248276021

2015-08-27

3248276021

0.0277

13.921

26.001

1923671

6698769752491288124089

72.504

1741142261980164
2² × 3 × 857 × 169305937571

2021-01-23

857

169305937571

609.50

725.60

1,355.2

exponent	prime factors	composite factor	digits	bits*
1923671	101573676143 362419634132399279	36812294545228873148712700897	29	94.894
1923671	101573676143 6698769752491288124089	680418669396074367345118082908727	33	109.068
1923671	362419634132399279 6698769752491288124089	2427765682835075515537736964836646131831	40	130.835
1923671	101573676143 362419634132399279 6698769752491288124089	24659708521937921449617885896143727309289567760783 3	51	167.399

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:02	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 101573676143	-	-	0.101	-	-	5.099%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:02

alpertron

Manual testing

500000

15000000

skipped known factor: 101573676143

0.101

-

-

5.099%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2015-08-27T11:20:00	TJAOI	Manual testing	2⁵⁸	2⁵⁹*	362419634132399279	58.330	18	0.008	0.212	0.016

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2015-08-27T11:20:00

TJAOI

Manual testing

2⁵⁸

2⁵⁹*

362419634132399279

58.330

0.008

0.212

0.016

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.890 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.890 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.628	0.002%
25	50000	0.978	37.601%
30	250000	0.062	93.981%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4950000	6698769752491288124089	4	0.277
50000	5000000		34	2.362
50000	6600000		213	16.70
50000	6750000		7	0.555

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-19T09:44:51	Gordon Spence	haswell	50000	5000000						3	0.208
2019-02-02T14:52:50	ATH	ec2-ECMCF	50000	5000000						3	0.208
2020-11-01T14:16:43	nordi	sweet16	50000	5000000						7	0.486
2021-01-23T16:42:25	seatsea	dt	50000	4950000	6698769752491288124089	72.504	4	2	3721713682092324	4	0.277
2021-03-24T10:48:10	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2021-07-12T19:08:03	Jonathan Webb	Desktop2021	50000	5000000						7	0.486
2021-09-26T21:09:24	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2022-02-01T10:44:27	Dylan Delgado	colab	50000	6750000						7	0.555
2022-02-10T10:47:34	TJAOI	Manual testing	50000	6600000						213	16.70

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:56

alpertron

Manual testing

101573676143

362419634132399279

8907645C01882F__

2017-10-20T07:19:12

Oliver Kruse

GTX-1

101573676143

362419634132399279

8907645C01882F__

2021-01-23T23:49:53

mrh

lanai

101573676143

362419634132399279

6698769752491288124089

1AED7470846751__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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