M1969819 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	15.0846	68.6567%	500000	15000000	0.1230	5.1137%	15.2076	70.2595%	1.6028%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4716%	0.0209	64.6880%	0.8949%
GPU72	2⁶²	0.3119	66.1290%	8000	100000	0.0012	1.1959%	0.3131	66.5341%	0.4051%
Difference	+5	+14.7727	+2.5277%	+492000	+14900000	+0.1217	+3.9178%	+14.8945	+3.7254%	+3.7254%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.0846

68.6567%

500000

15000000

0.1230

5.1137%

15.2076

70.2595%

1.6028%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4716%

0.0209

64.6880%

0.8949%

GPU72

2⁶²

0.3119

66.1290%

8000

100000

0.0012

1.1959%

0.3131

66.5341%

0.4051%

Difference

+14.7727

+2.5277%

+492000

+14900000

+0.1217

+3.9178%

+14.8945

+3.7254%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1969819	1413552077744503	16	50.328	358802529 3 × 29 × 4124167	-	29	4124167	0.0001	0.0214	0.0400
1969819	15692471667838039	17	53.801	3983226801 3 × 1327742267	2014-10-13	3	1327742267	0.0008	6.8966	12.881
1969819	96784733255519443681	20	66.391	24566910273360 2⁴ × 3⁴ × 5 × 7 × 13 × 31 × 1343917	2015-09-29	81	1343917	8.8769	0.0070	0.0130
1969819	1637896554953840134893143	25	80.438	415747983686277809 7 × 223 × 5464489 × 48739121	2021-11-15	5464489	48739121	234,869	0.7457	1.0603

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1969819

1413552077744503

50.328

358802529
3 × 29 × 4124167

4124167

0.0001

0.0214

0.0400

1969819

15692471667838039

53.801

3983226801
3 × 1327742267

2014-10-13

1327742267

0.0008

6.8966

12.881

1969819

96784733255519443681

66.391

24566910273360
2⁴ × 3⁴ × 5 × 7 × 13 × 31 × 1343917

2015-09-29

1343917

8.8769

0.0070

0.0130

1969819

1637896554953840134893143

80.438

415747983686277809
7 × 223 × 5464489 × 48739121

2021-11-15

5464489

48739121

234,869

0.7457

1.0603

exponent	prime factors	composite factor	digits	bits*
1969819	1413552077744503 15692471667838039	22182125931019206362177426549617	32	104.129
1969819	1413552077744503 96784733255519443681	136810260787287005592096067815835543	36	116.720
1969819	15692471667838039 96784733255519443681	1518791684491500922404416945289981559	37	120.192
1969819	1413552077744503 1637896554953840134893143	2315252078385564260656961302656360642929	40	130.766
1969819	15692471667838039 1637896554953840134893143	25702645283462666000675065832885095666577	41	134.239
1969819	96784733255519443681 1637896554953840134893143	158523381171341661309148504688324895741579383	45	146.830
1969819	1413552077744503 15692471667838039 96784733255519443681	21468911412740347831911553182215044290353751836201 77	52	170.521
1969819	1413552077744503 15692471667838039 1637896554953840134893143	36332027643968601798685327935687050419614070209482 576231	56	184.567
1969819	1413552077744503 96784733255519443681 1637896554953840134893143	22408105482583383107238478877327088321228994195432 1566381649	60	197.158
1969819	15692471667838039 96784733255519443681 1637896554953840134893143	24876236677211690683039730322188125958359625288612 18905549937	61	200.630
1969819	1413552077744503 15692471667838039 96784733255519443681 1637896554953840134893143	35163856041536596768586494819044032977236890180036 10039316544332407793746311	76	250.959

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-09-29T01:17:26	alpertron	Manual testing	500000	15000000	12		96784733255519443681	20	66.391	0.123	0.259	0.246	5.114%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-09-29T01:17:26

alpertron

Manual testing

500000

15000000

96784733255519443681

66.391

0.123

0.259

0.246

5.114%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-10-13T11:49:00	TJAOI	Manual testing	2⁵³	2⁵⁴*	15692471667838039	53.801	17	0.000	0.281	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-10-13T11:49:00

TJAOI

Manual testing

2⁵³

2⁵⁴*

15692471667838039

53.801

0.000

0.281

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.385 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.385 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.266	28.208%
25	50000	0.114	89.208%
30	250000	0.007	99.297%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.689
50000	5000000	1637896554953840134893143	4	0.338
50000	6700000		7	0.672
50000	7000000		7	0.686

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-22T05:27:16	Oliver Kruse	ECM-HTC	50000	5000000						3	0.253
2019-03-26T07:50:48	ATH	ec2-ECMCF	50000	5000000						3	0.253
2021-03-26T00:00:59	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.591
2021-05-03T08:29:45	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.591
2021-08-11T05:16:13	Ahmed Azhad	c5.4xlarge.azf2	50000	6700000						7	0.672
2021-11-15T09:01:12	MarkS	desktop-i7	50000	5000000	1637896554953840134893143	80.438	4	2	6875439987286229	4	0.338
2022-02-13T07:25:45	happy5214	Focus	50000	7000000						7	0.686

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T10:17:06

Oliver Kruse

GTX-0

1413552077744503

15692471667838039

96784733255519443681

731EC023FE9057A8

2017-10-05T21:08:06

Oliver Kruse

Manual testing

1413552077744503

15692471667838039

96784733255519443681

731EC023FE9057__

2017-11-15T20:40:01

kkmrkkblmbrbk

c4.xlarge

1413552077744503

15692471667838039

96784733255519443681

731EC023FE9057__

2021-11-15T09:15:34

MarkS

desktop-i7

1413552077744503

15692471667838039

96784733255519443681

1637896554953840134893143

D1D88DB11DB2E30C

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

10⁷

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