M1947641 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	15.2564	68.6567%	500000	15000000	0.1015	5.1067%	15.3578	70.2573%	1.6006%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4662%	0.0209	64.6860%	0.8929%
GPU72	2⁶²	0.3154	66.1290%	8000	90000	0.0010	1.1528%	0.3164	66.5195%	0.3905%
Difference	+5	+14.9409	+2.5277%	+492000	+14910000	+0.1005	+3.9539%	+15.0414	+3.7378%	+3.7378%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2564

68.6567%

500000

15000000

0.1015

5.1067%

15.3578

70.2573%

1.6006%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4662%

0.0209

64.6860%

0.8929%

GPU72

2⁶²

0.3154

66.1290%

8000

90000

0.0010

1.1528%

0.3164

66.5195%

0.3905%

Difference

+14.9409

+2.5277%

+492000

+14910000

+0.1005

+3.9539%

+15.0414

+3.7378%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1947641	214511898192223	15	47.608	55069671 3 × 31 × 103 × 5749	-	103	5749	1.773e-5	3.230e-5	4.598e-5
1947641	79102037377893781122017	23	76.066	20307140119224688 2⁴ × 53411 × 23762825213	2021-12-06	53411	23762825213	8,313.5	101.85	190.21
1947641	1140184983693690389300473	25	79.916	292709227135208796 2² × 3² × 11 × 1699 × 435058690399	2022-04-14	1699	435058690399	95,192	1,864.6	3,482.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1947641

214511898192223

47.608

55069671
3 × 31 × 103 × 5749

103

5749

1.773e-5

3.230e-5

4.598e-5

1947641

79102037377893781122017

76.066

20307140119224688
2⁴ × 53411 × 23762825213

2021-12-06

53411

23762825213

8,313.5

101.85

190.21

1947641

1140184983693690389300473

79.916

292709227135208796
2² × 3² × 11 × 1699 × 435058690399

2022-04-14

1699

435058690399

95,192

1,864.6

3,482.5

exponent	prime factors	composite factor	digits	bits*
1947641	214511898192223 79102037377893781122017	16968328188804169161771312546883473791	38	123.674
1947641	214511898192223 1140184983693690389300473	244583245142402354153755603230258821479	39	127.524
1947641	79102037377893781122017 1140184983693690389300473	90190955197851508507544377574971707289688814041	47	155.982
1947641	214511898192223 79102037377893781122017 1140184983693690389300473	19347032999260868593113102272681521117605369819649 812719403143	62	203.590

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:10	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 214511898192223	-	-	0.101	-	-	5.107%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:10

alpertron

Manual testing

500000

15000000

skipped known factor: 214511898192223

0.101

-

-

5.107%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.971 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:	20.971 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.069	0.012%
25	50000	0.806	44.664%
30	250000	0.050	95.126%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	2.713
50000	5000000	79102037377893781122017	3	0.209
50000	7500000		190	15.88
50000	7500000	1140184983693690389300473	26	2.173

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-06-26T11:23:00	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-11T18:26:18	ATH	ec2-ECMCF	50000	5000000						3	0.209
2020-11-13T10:19:16	Tsurumaki Kokoro	Baidu_HK_1	50000	5000000						7	0.487
2021-02-11T18:26:24	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2021-07-23T03:49:49	TBB_Nozomi	Nozomi_Power	50000	5000000						7	0.487
2021-08-30T05:00:54	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2021-12-06T11:02:33	MarkS	desktop-i7	50000	5000000	79102037377893781122017	76.066	3	2	2011293806717811	3	0.209
2022-02-13T18:20:04	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2022-04-14T10:51:43	TJAOI	Manual testing	50000	7500000	1140184983693690389300473	79.916	26	2		26	2.173
2022-04-28T10:17:50	TJAOI	Manual testing	50000	7500000						190	15.88

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T04:52:05

Oliver Kruse

GTX-3

214511898192223

482C8B0E32E721__

2017-11-11T10:14:15

kkmrkkblmbrbk

c4.xlarge

214511898192223

482C8B0E32E721__

2021-12-08T13:41:15

SRJ2877

LTOS

214511898192223

79102037377893781122017

2B1CB0964BCA1AE0

2022-04-20T11:21:58

Poao

office-CN2

214511898192223

79102037377893781122017

1140184983693690389300473

2B1CB0964BCA1AE0

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

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