M1819343 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	16.3322	68.6567%	500000	15000000	0.1015	5.0650%	16.4337	70.2443%	1.5875%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8759%	0.0118	64.2175%	1.0596%
GPU72	2⁶¹	0.1688	65.5738%	9000	130000	0.0012	1.5578%	0.1701	66.1100%	0.5363%
Difference	+6	+16.1634	+3.0829%	+491000	+14870000	+0.1002	+3.5072%	+16.2636	+4.1342%	+4.1342%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3322

68.6567%

500000

15000000

0.1015

5.0650%

16.4337

70.2443%

1.5875%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8759%

0.0118

64.2175%

1.0596%

GPU72

2⁶¹

0.1688

65.5738%

9000

130000

0.0012

1.5578%

0.1701

66.1100%

0.5363%

Difference

+16.1634

+3.0829%

+491000

+14870000

+0.1002

+3.5072%

+16.2636

+4.1342%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1819343	43664233	8	25.380	12 2² × 3	-	4	4	2.463e-12	3.146e-7	6.404e-7
1819343	106450603105153	15	46.597	29255232 2⁶ × 3 × 17 × 8963	2014-02-18	64	8963	6.705e-6	4.317e-5	7.173e-5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1819343

43664233

25.380

12
2² × 3

2.463e-12

3.146e-7

6.404e-7

1819343

106450603105153

46.597

29255232
2⁶ × 3 × 17 × 8963

2014-02-18

8963

6.705e-6

4.317e-5

7.173e-5

exponent	prime factors	composite factor	digits	bits*
1819343	43664233 106450603105153	4648083936973924092649	22	71.977

exponent

prime factors

composite factor

digits

bits*

1819343

43664233
106450603105153

4648083936973924092649

71.977

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:50	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 43664233 skipped known factor: 106450603105153	-	-	0.101	-	-	5.065%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-02-18T11:16:00	TJAOI	Manual testing	?	?	106450603105153	46.597	15	1.55248e-6	0.211	3.32335e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-02-18T11:16:00

TJAOI

Manual testing

106450603105153

46.597

1.55248e-6

0.211

3.32335e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.151 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.151 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	10.321	0.003%
25	50000	0.950	38.676%
30	250000	0.060	94.151%
35	1000000	0.003	99.717%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	2.968
50000	6600000		208	16.18

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-07-04T14:00:59	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-03T15:28:42	Ismo Laitela	6600K	50000	5000000						3	0.207
2019-10-07T22:06:42	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-03T08:02:16	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-02T14:55:13	kracker	O0	50000	5000000						3	0.207
2020-06-29T22:18:25	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-07-27T08:12:04	Ahmed Azhad	c5.large.az	50000	5000000						3	0.207
2020-10-06T05:13:31	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2020-12-02T22:57:25	MarkS	desktop-i7	50000	5000000						17	1.173
2021-03-26T16:50:04	TJAOI	Manual testing	50000	6600000						208	16.18

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

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