M1665973 Mersenne number exponent details

Residue

Status

L-L

AC37B8A64DF7B56C

double-checked

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	17.8358	68.6567%	500000	15000000	0.0880	5.0115%	17.9238	70.2275%	1.5708%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5683%	0.0124	64.1041%	0.9462%
GPU72	2⁶¹	0.1844	65.5738%	7000	80000	0.0007	1.2061%	0.1851	65.9890%	0.4152%
Difference	+6	+17.6514	+3.0829%	+493000	+14920000	+0.0873	+3.8054%	+17.7387	+4.2385%	+4.2385%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.8358

68.6567%

500000

15000000

0.0880

5.0115%

17.9238

70.2275%

1.5708%

PrimeNet

2⁵⁷

0.0115

63.1579%

7000

120000

0.0009

2.5683%

0.0124

64.1041%

0.9462%

GPU72

2⁶¹

0.1844

65.5738%

7000

80000

0.0007

1.2061%

0.1851

65.9890%

0.4152%

Difference

+17.6514

+3.0829%

+493000

+14920000

+0.0873

+3.8054%

+17.7387

+4.2385%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1665973	7724845184770411039	19	62.744	2318418481203 3² × 11 × 40013 × 585269	2008-05-29	40013	585269	0.4151	0.0048	0.0056

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1665973

7724845184770411039

62.744

2318418481203
3² × 11 × 40013 × 585269

2008-05-29

40013

585269

0.4151

0.0048

0.0056

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:07	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 7724845184770411039	-	-	0.088	-	-	5.012%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.710 GHz-days
Estimated T-Level:	24.429

Digits	B1	Curves	Complete	FacMiss
20	11000	248 / 100	2.480	8.270%
25	50000	248 / 280	0.886	41.177%

New Calculation Method

Total ECM effort:	14.710 GHz-days
Estimated T-Level:	24.429

Digits	B1	Complete	FacMiss
20	11000	9.538	0.007%
25	50000	0.883	41.372%
30	250000	0.056	94.585%
35	1000000	0.003	99.740%

ECM Summary

B1	B2	factor	curves	GHz-days
		7724845184770411039	1	0.00000e+0
50000	5000000		248	14.71

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-29T21:01:00	James Heinrich	Q6600			7724845184770411039	62.744		1		1	-
2015-02-19T13:55:00	Richard B. Woods	Puttputt	50000	5000000						2	0.119
2019-12-23T11:27:00	TJAOI	Manual testing	50000	5000000						246	14.59

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	AC37B8A64DF7B56C	0.078

date

userid

compid

res64

spent (GHz-days)

1998-11-21T00:00:00

ANONYMOUS

v4_computers

AC37B8A64DF7B56C

0.078

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T21:45:39

Oliver Kruse

GTX-1

7724845184770411039

29DDA9AAB87ABA__

2017-11-10T20:57:47

kkmrkkblmbrbk

c4.xlarge

7724845184770411039

29DDA9AAB87ABA__

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)

10³

10⁴

10⁵

10⁶

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