M1916741 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	15.5023	68.6567%	500000	15000000	0.1015	5.0969%	15.6038	70.2543%	1.5975%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0919%	0.0114	64.2970%	1.1391%
GPU72	2⁶¹	0.1603	65.5738%	10000	170000	0.0015	1.7609%	0.1617	66.1800%	0.6062%
Difference	+6	+15.3421	+3.0829%	+490000	+14830000	+0.1000	+3.3360%	+15.4421	+4.0743%	+4.0743%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.5023

68.6567%

500000

15000000

0.1015

5.0969%

15.6038

70.2543%

1.5975%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0919%

0.0114

64.2970%

1.1391%

GPU72

2⁶¹

0.1603

65.5738%

10000

170000

0.0015

1.7609%

0.1617

66.1800%

0.6062%

Difference

+15.3421

+3.0829%

+490000

+14830000

+0.1000

+3.3360%

+15.4421

+4.0743%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1916741	5627551577	10	32.390	1468 2² × 367	-	4	367	3.934e-10	1.870e-6	2.912e-6
1916741	14512286730312431271361	23	73.620	3785667111600480 2⁵ × 3³ × 5 × 876311831389	2021-04-19	32	876311831389	1,386.8	3,755.7	7,014.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1916741

5627551577

32.390

1468
2² × 367

367

3.934e-10

1.870e-6

2.912e-6

1916741

14512286730312431271361

73.620

3785667111600480
2⁵ × 3³ × 5 × 876311831389

2021-04-19

876311831389

1,386.8

3,755.7

7,014.5

exponent	prime factors	composite factor	digits	bits*
1916741	5627551577 14512286730312431271361	81668642075045896303851710486297	32	106.010

exponent

prime factors

composite factor

digits

bits*

1916741

5627551577
14512286730312431271361

81668642075045896303851710486297

106.010

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:57	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 5627551577	-	-	0.101	-	-	5.097%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.867 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:	20.867 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.055	0.012%
25	50000	0.805	44.709%
30	250000	0.050	95.132%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	1.875
50000	5000000	14512286730312431271361	19	1.319
50000	7500000		212	17.67

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-19T01:03:20	alpertron	laptop2	50000	5000000						3	0.208
2019-01-30T21:43:43	tottenhoff	i3-8100-01	50000	5000000						3	0.208
2020-10-31T05:11:44	nordi	sweet16	50000	5000000						7	0.486
2021-01-18T06:52:26	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2021-04-19T14:37:21	MarkS	desktop-i7	50000	5000000	14512286730312431271361	73.620	19	2	2292409068493992	19	1.319
2022-01-27T04:48:25	MarkS	laptop64	50000	5000000						7	0.486
2022-03-03T12:26:25	TJAOI	Manual testing	50000	7500000						212	17.67

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:14:49

alpertron

Manual testing

5627551577

DCC7C0C3948EE9__

2017-10-20T06:22:07

Oliver Kruse

GTX-1

5627551577

DCC7C0C3948EE9__

2021-04-19T15:04:46

XZT

800G3Mini2

5627551577

14512286730312431271361

C8B55F9F046C29E3

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

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