M1923293 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	15.4495	68.6567%	500000	15000000	0.1015	5.0990%	15.5510	70.2549%	1.5982%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0938%	0.0114	64.2977%	1.1398%
GPU72	2⁶¹	0.1597	65.5738%	10000	170000	0.0015	1.7621%	0.1612	66.1804%	0.6066%
Difference	+6	+15.2898	+3.0829%	+490000	+14830000	+0.1000	+3.3369%	+15.3898	+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

15.4495

68.6567%

500000

15000000

0.1015

5.0990%

15.5510

70.2549%

1.5982%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0938%

0.0114

64.2977%

1.1398%

GPU72

2⁶¹

0.1597

65.5738%

10000

170000

0.0015

1.7621%

0.1612

66.1804%

0.6066%

Difference

+15.2898

+3.0829%

+490000

+14830000

+0.1000

+3.3369%

+15.3898

+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
1923293	4025633038543	13	41.872	1046547 3³ × 83 × 467	-	83	467	2.323e-7	8.175e-6	1.329e-5
1923293	1152161231193627932351	22	69.965	299528265114475 5² × 4363 × 2746076233	2019-02-16	4363	2746076233	123.37	11.769	21.981

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1923293

4025633038543

41.872

1046547
3³ × 83 × 467

467

2.323e-7

8.175e-6

1.329e-5

1923293

1152161231193627932351

69.965

299528265114475
5² × 4363 × 2746076233

2019-02-16

4363

2746076233

123.37

11.769

21.981

exponent	prime factors	composite factor	digits	bits*
1923293	4025633038543 1152161231193627932351	4638178318021448328089954579604593	34	111.837

exponent

prime factors

composite factor

digits

bits*

1923293

4025633038543
1152161231193627932351

4638178318021448328089954579604593

111.837

	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: 4025633038543	-	-	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: 4025633038543

0.101

-

-

5.099%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.882 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:	19.882 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.625	0.002%
25	50000	0.978	37.607%
30	250000	0.062	93.982%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		38	2.640
50000	5000000	1152161231193627932351	1	0.069
50000	6600000		212	16.62
50000	6750000		7	0.555

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-19T18:15:23	alpertron	laptop2	50000	5000000						3	0.208
2019-02-16T05:22:47	ATH	ec2-ECMCF	50000	5000000	1152161231193627932351	69.965	1	2	7956647423319231	1	0.069
2020-10-21T09:17:03	nordi	sweet16	50000	5000000						7	0.486
2021-01-12T07:14:31	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2021-04-08T05:34:40	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-07-19T23:00:08	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-10-04T05:09:20	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2022-02-16T07:15:09	Dylan Delgado	colab	50000	6750000						7	0.555
2022-03-03T12:27:41	TJAOI	Manual testing	50000	6600000						212	16.62

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T23:15:01

Oliver Kruse

GTX-2

4025633038543

169A5BB911C7BC__

2017-11-10T02:29:52

ATH

ec2-1xf

4025633038543

169A5BB911C7BC__

2019-02-17T02:08:38

artorollo

fourth

4025633038543

1152161231193627932351

B7DB308F17A81D9B

2019-02-17T02:52:08

ATH

ec2-PRPCFDC

4025633038543

1152161231193627932351

B7DB308F17A81D9B

2019-02-17T14:06:52

alex

Manual testing

4025633038543

1152161231193627932351

B7DB308F17A81D9B

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

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