M1672651 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	17.7646	68.6567%	500000	15000000	0.0880	5.0139%	17.8526	70.2282%	1.5715%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5703%	0.0124	64.1048%	0.9469%
GPU72	2⁶¹	0.1836	65.5738%	7000	80000	0.0007	1.2072%	0.1844	65.9894%	0.4156%
Difference	+6	+17.5809	+3.0829%	+493000	+14920000	+0.0873	+3.8067%	+17.6682	+4.2389%	+4.2389%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.7646

68.6567%

500000

15000000

0.0880

5.0139%

17.8526

70.2282%

1.5715%

PrimeNet

2⁵⁷

0.0115

63.1579%

7000

120000

0.0009

2.5703%

0.0124

64.1048%

0.9469%

GPU72

2⁶¹

0.1836

65.5738%

7000

80000

0.0007

1.2072%

0.1844

65.9894%

0.4156%

Difference

+17.5809

+3.0829%

+493000

+14920000

+0.0873

+3.8067%

+17.6682

+4.2389%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1672651	25762170703	11	34.585	7701 3 × 17 × 151	-	17	151	2.281e-9	1.658e-6	2.361e-6
1672651	273257728853990166449	21	67.889	81684023999624 2³ × 1248151 × 8180503	2019-03-19	1248151	8180503	22.112	0.1109	0.1733

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1672651

25762170703

34.585

7701
3 × 17 × 151

151

2.281e-9

1.658e-6

2.361e-6

1672651

273257728853990166449

67.889

81684023999624
2³ × 1248151 × 8180503

2019-03-19

1248151

8180503

22.112

0.1109

0.1733

exponent	prime factors	composite factor	digits	bits*
1672651	25762170703 273257728853990166449	7039712256650583230742521343647	31	102.473

exponent

prime factors

composite factor

digits

bits*

1672651

25762170703
273257728853990166449

7039712256650583230742521343647

102.473

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:12	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 25762170703	-	-	0.088	-	-	5.014%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.894 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:	14.894 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	14.83
50000	5000000	273257728853990166449	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-08-27T23:53:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-02-03T20:07:07	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-03-19T05:15:19	Chang Chia-Tche	exbpc13	50000	5000000	273257728853990166449	67.889	1	2		1	0.059
2019-12-16T13:28:38	TJAOI	Manual testing	50000	5000000						246	14.60

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T22:59:11

Oliver Kruse

GTX-0

25762170703

5F27B326AE5AF1__

2017-11-03T00:42:07

kkmrkkblmbrbk

c4.xlarge

25762170703

5F27B326AE5AF1__

2019-03-21T10:39:53

-Anonymous-

25762170703

273257728853990166449

E787235D78EE04CD

2019-03-22T03:52:52

kkmrkkblmbrbk

c5.large

25762170703

273257728853990166449

E787235D78EE04CD

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

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