M1915841 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	15.5096	68.6567%	500000	15000000	0.1015	5.0966%	15.6111	70.2542%	1.5975%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0916%	0.0114	64.2969%	1.1390%
GPU72	2⁶¹	0.1603	65.5738%	10000	170000	0.0015	1.7608%	0.1618	66.1799%	0.6062%
Difference	+6	+15.3493	+3.0829%	+490000	+14830000	+0.1000	+3.3359%	+15.4493	+4.0742%	+4.0742%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.5096

68.6567%

500000

15000000

0.1015

5.0966%

15.6111

70.2542%

1.5975%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0916%

0.0114

64.2969%

1.1390%

GPU72

2⁶¹

0.1603

65.5738%

10000

170000

0.0015

1.7608%

0.1618

66.1799%

0.6062%

Difference

+15.3493

+3.0829%

+490000

+14830000

+0.1000

+3.3359%

+15.4493

+4.0742%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1915841	253258853473	12	37.882	66096 2⁴ × 3⁵ × 17	-	243	243	1.249e-8	1.911e-5	3.890e-5
1915841	827286355170653969359	21	69.487	215906840695719 3⁴ × 9239 × 288507041	2020-10-30	9239	288507041	104.18	1.2372	2.3094

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1915841

253258853473

37.882

66096
2⁴ × 3⁵ × 17

243

1.249e-8

1.911e-5

3.890e-5

1915841

827286355170653969359

69.487

215906840695719
3⁴ × 9239 × 288507041

2020-10-30

9239

288507041

104.18

1.2372

2.3094

exponent	prime factors	composite factor	digits	bits*
1915841	253258853473 827286355170653969359	209517593804376889535476812733807	33	107.369

exponent

prime factors

composite factor

digits

bits*

1915841

253258853473
827286355170653969359

209517593804376889535476812733807

107.369

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:56	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 253258853473	-	-	0.101	-	-	5.097%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:56

alpertron

Manual testing

500000

15000000

skipped known factor: 253258853473

0.101

-

-

5.097%

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.812 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:	21.812 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.104	0.011%
25	50000	0.808	44.588%
30	250000	0.050	95.120%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		7	0.293
50000	5000000		34	2.361
50000	5000000	827286355170653969359	3	0.208
50000	5750000		7	0.515
50000	8000000		214	18.43

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T19:44:20	alpertron		50000	5000000						3	0.208
2018-09-28T16:55:00	alpertron	Manual testing	50000	5000000						3	0.208
2020-10-30T14:15:08	nordi	sweet16	50000	5000000	827286355170653969359	69.487	3	2	4055564771484674	3	0.208
2020-11-16T02:37:59	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2021-02-13T00:51:48	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-05-29T12:01:47	LordJulius	Ev	50000	5750000						7	0.515
2021-09-04T01:37:05	Alvin Bunk	BADCAT	50000	5000000						7	0.486
2021-12-15T06:29:46	JackBlock	school4	50000	50000						7	0.293
2022-01-05T23:13:06	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2022-01-25T11:46:55	TJAOI	Manual testing	50000	8000000						214	18.43

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:14:46

alpertron

Manual testing

253258853473

BC8653BC5FB6BB__

2017-10-20T05:05:12

Oliver Kruse

Threadripper

253258853473

BC8653BC5FB6BB__

2020-10-30T18:38:20

mrh

253258853473

827286355170653969359

5A570775FCB74A46

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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