M1699501 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	17.4839	68.6567%	500000	15000000	0.0880	5.0236%	17.5719	70.2313%	1.5746%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7311%	0.0123	64.1641%	1.0062%
GPU72	2⁶¹	0.1807	65.5738%	7000	100000	0.0008	1.3012%	0.1816	66.0217%	0.4480%
Difference	+6	+17.3032	+3.0829%	+493000	+14900000	+0.0872	+3.7223%	+17.3904	+4.2095%	+4.2095%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.4839

68.6567%

500000

15000000

0.0880

5.0236%

17.5719

70.2313%

1.5746%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7311%

0.0123

64.1641%

1.0062%

GPU72

2⁶¹

0.1807

65.5738%

7000

100000

0.0008

1.3012%

0.1816

66.0217%

0.4480%

Difference

+17.3032

+3.0829%

+493000

+14900000

+0.0872

+3.7223%

+17.3904

+4.2095%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1699501	270411003113	12	37.976	79556 2² × 19889	-	4	19889	1.314e-8	7.420e-5	0.0001
1699501	7539865431513209	16	52.743	2218258604 2² × 29² × 223 × 2957	2014-08-22	841	2957	0.0005	6.526e-5	0.0001
1699501	54071881783527468951023	23	75.517	15908164156281011 47 × 338471577793213	2019-05-01	47	338471577793213	7,203.0	1,258,416	2,350,371

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1699501

270411003113

37.976

79556
2² × 19889

19889

1.314e-8

7.420e-5

0.0001

1699501

7539865431513209

52.743

2218258604
2² × 29² × 223 × 2957

2014-08-22

841

2957

0.0005

6.526e-5

0.0001

1699501

54071881783527468951023

75.517

15908164156281011
47 × 338471577793213

2019-05-01

338471577793213

7,203.0

1,258,416

2,350,371

exponent	prime factors	composite factor	digits	bits*
1699501	270411003113 7539865431513209	2038862574672519447199619617	28	90.720
1699501	270411003113 54071881783527468951023	14621631793291214398636091297534599	35	113.494
1699501	7539865431513209 54071881783527468951023	407694712276487564760986498598798562807	39	128.261
1699501	270411003113 7539865431513209 54071881783527468951023	11024513611055091819128890917355068830526360301819 1	51	166.237

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:55	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 270411003113 skipped known factor: 7539865431513209	-	-	0.088	-	-	5.024%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-08-22T11:32:00	TJAOI	Manual testing	?	?	7539865431513209	52.743	16	0.000	0.173	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-08-22T11:32:00

TJAOI

Manual testing

7539865431513209

52.743

0.000

0.173

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.632 GHz-days
Estimated T-Level:	24.696

Digits	B1	Curves	Complete	FacMiss
20	11000	263 / 100	2.630	7.113%
25	50000	263 / 280	0.939	39.025%

New Calculation Method

Total ECM effort:	15.632 GHz-days
Estimated T-Level:	24.696

Digits	B1	Complete	FacMiss
20	11000	8.484	0.021%
25	50000	0.767	46.451%
30	250000	0.047	95.388%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		261	15.51
50000	5000000	54071881783527468951023	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-12-02T07:41:39	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-05T16:05:55	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-05-01T13:55:33	Chang Chia-Tche	exbpc13	50000	5000000	54071881783527468951023	75.517	2	2		2	0.119
2020-01-29T21:53:15	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-05T17:29:45	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-13T12:26:51	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-21T13:46:03	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-24T10:26:44	TJAOI	Manual testing	50000	5000000						245	14.56

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T03:05:43

Oliver Kruse

GTX-2

270411003113

7539865431513209

6FC94D98C873B2__

2017-11-03T13:48:19

kkmrkkblmbrbk

c4.xlarge

270411003113

7539865431513209

6FC94D98C873B2__

2019-05-04T12:06:31

ANONYMOUS

270411003113

7539865431513209

54071881783527468951023

32AC6E5628567F2A

2019-05-05T02:58:38

kkmrkkblmbrbk

c5.large

270411003113

7539865431513209

54071881783527468951023

32AC6E5628567F2A

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

10¹³

10¹⁴

10¹⁵

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