M1750607 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	16.9735	68.6567%	500000	15000000	0.1015	5.0416%	17.0750	70.2369%	1.5802%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8027%	0.0122	64.1905%	1.0326%
GPU72	2⁶¹	0.1755	65.5738%	8000	110000	0.0011	1.4128%	0.1765	66.0601%	0.4864%
Difference	+6	+16.7980	+3.0829%	+492000	+14890000	+0.1004	+3.6288%	+16.8984	+4.1768%	+4.1768%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9735

68.6567%

500000

15000000

0.1015

5.0416%

17.0750

70.2369%

1.5802%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8027%

0.0122

64.1905%

1.0326%

GPU72

2⁶¹

0.1755

65.5738%

8000

110000

0.0011

1.4128%

0.1765

66.0601%

0.4864%

Difference

+16.7980

+3.0829%

+492000

+14890000

+0.1004

+3.6288%

+16.8984

+4.1768%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1750607	254106432070097	15	47.852	72576664 2³ × 9072083	-	8	9072083	1.322e-5	0.0389	0.0726
1750607	106633693709718140897	21	66.531	30456205678864 2⁴ × 7² × 38847201121	2018-03-19	49	38847201121	12.213	166.49	310.96

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1750607

254106432070097

47.852

72576664
2³ × 9072083

9072083

1.322e-5

0.0389

0.0726

1750607

106633693709718140897

66.531

30456205678864
2⁴ × 7² × 38847201121

2018-03-19

38847201121

12.213

166.49

310.96

exponent	prime factors	composite factor	digits	bits*
1750607	254106432070097 106633693709718140897	27096307447032022536980062026457009	35	114.384

exponent

prime factors

composite factor

digits

bits*

1750607

254106432070097
106633693709718140897

27096307447032022536980062026457009

114.384

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:29:16	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 254106432070097	-	-	0.101	-	-	5.042%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.252 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:	17.252 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	9.654	0.006%
25	50000	0.893	40.933%
30	250000	0.056	94.522%
35	1000000	0.003	99.737%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	17.18
50000	5000000	106633693709718140897	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-12T15:53:48	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-19T08:21:42	ATH	ec2-ECMCF	50000	5000000	106633693709718140897	66.531	1	2		1	0.069
2018-09-18T04:46:18	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-07-06T08:24:40	TJAOI	Manual testing	50000	5000000						246	16.91

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T06:28:20

Oliver Kruse

GTX-0

254106432070097

2672C808B9BEA0__

2017-11-03T23:38:03

Chang Chia-Tche

exbpc13

254106432070097

2672C808B9BEA0__

2018-03-22T04:55:22

Jack Rhys-Burgess

254106432070097

106633693709718140897

8231162A742E2D__

2018-03-27T00:46:02

kracker

GRID-11

254106432070097

106633693709718140897

8231162A742E2D__

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

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