M1694621 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	17.5343	68.6567%	500000	15000000	0.0880	5.0218%	17.6223	70.2307%	1.5740%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7297%	0.0123	64.1636%	1.0057%
GPU72	2⁶¹	0.1813	65.5738%	7000	100000	0.0008	1.3004%	0.1821	66.0215%	0.4477%
Difference	+6	+17.3530	+3.0829%	+493000	+14900000	+0.0872	+3.7214%	+17.4402	+4.2093%	+4.2093%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.5343

68.6567%

500000

15000000

0.0880

5.0218%

17.6223

70.2307%

1.5740%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7297%

0.0123

64.1636%

1.0057%

GPU72

2⁶¹

0.1813

65.5738%

7000

100000

0.0008

1.3004%

0.1821

66.0215%

0.4477%

Difference

+17.3530

+3.0829%

+493000

+14900000

+0.0872

+3.7214%

+17.4402

+4.2093%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1694621	35281666906559	14	45.004	10409899 17 × 113 × 5419	-	113	5419	3.388e-6	2.744e-5	3.763e-5
1694621	21660895415137747583	20	64.232	6391073701771 11 × 646003 × 899387	2017-08-17	646003	899387	2.3156	0.0450	0.0897
1694621	193998520628779914208207	24	77.360	57239500935247443 3² × 6359944548360827	2018-03-03	9	6359944548360827	30,271	23,645,876	44,163,912

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1694621

35281666906559

45.004

10409899
17 × 113 × 5419

113

5419

3.388e-6

2.744e-5

3.763e-5

1694621

21660895415137747583

64.232

6391073701771
11 × 646003 × 899387

2017-08-17

646003

899387

2.3156

0.0450

0.0897

1694621

193998520628779914208207

77.360

57239500935247443
3² × 6359944548360827

2018-03-03

6359944548360827

30,271

23,645,876

44,163,912

exponent	prime factors	composite factor	digits	bits*
1694621	35281666906559 21660895415137747583	764232496934701040867574589096897	33	109.236
1694621	35281666906559 193998520628779914208207	6844591185189827783308704077539929713	37	122.364
1694621	21660895415137747583 193998520628779914208207	4202181666031444588038834435092032873013681	43	141.592
1694621	35281666906559 21660895415137747583 193998520628779914208207	14825997382177058242849412585611348972928733579895 5633679	57	186.596

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:50	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 35281666906559	-	-	0.088	-	-	5.022%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-08-17T11:41:06	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	21660895415137747583	64.232	20	0.215	0.162	0.438

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.093 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	15.093 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		252	14.97
50000	5000000	193998520628779914208207	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-01-08T23:02:54	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-03T18:01:13	Chang Chia-Tche	exbpc13	50000	5000000	193998520628779914208207	77.360	2	2		2	0.119
2018-11-24T02:32:37	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-01-28T05:43:10	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-03T10:37:34	TJAOI	Manual testing	50000	5000000						245	14.56

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:10:04

alpertron

Manual testing

35281666906559

21660895415137747583

A0C57EDC9E3E5C__

2017-10-18T15:15:59

Oliver Kruse

Threadripper

35281666906559

21660895415137747583

A0C57EDC9E3E5C__

2018-03-08T11:26:25

trebor

Desktop

35281666906559

21660895415137747583

193998520628779914208207

C0087C8FB7F21E__

2018-03-11T16:39:31

Oliver Kruse

GTX-6

35281666906559

21660895415137747583

193998520628779914208207

C0087C8FB7F21E__

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

10¹⁶

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