M1 726 661 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
Actual	2⁶⁷	17.2089	68.6567%	500000	15000000	0.1015	5.0332%	17.3104	70.2343%
Target	2⁶¹	0.1779	65.5738%	7000	550000	0.0029	1.3448%	0.1808	66.0367%
Difference	+6	+17.0310	+3.0829%	+493000	+14450000	+0.0986	+3.6884%	+17.1296	+4.1976%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

17.2089

68.6567%

500000

15000000

0.1015

5.0332%

17.3104

70.2343%

Target

2⁶¹

0.1779

65.5738%

7000

550000

0.0029

1.3448%

0.1808

66.0367%

Difference

+17.0310

+3.0829%

+493000

+14450000

+0.0986

+3.6884%

+17.1296

+4.1976%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1726661	10359967	8	23.305	3 3	-	1	3	6.476e-13	8.723e-8	1.601e-7
1726661	225383074265950537	18	57.645	65265583188 2² × 3 × 13 × 418369123	2015-07-06	13	418369123	0.0179	1.7930	3.3489

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1726661

10359967

23.305

3
3

6.476e-13

8.723e-8

1.601e-7

1726661

225383074265950537

57.645

65265583188
2² × 3 × 13 × 418369123

2015-07-06

418369123

0.0179

1.7930

3.3489

exponent	prime factors	composite factor	digits	bits*
1726661	10359967 225383074265950537	2334961211753796786952279	25	80.950

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 10359967	-	-	0.101	-	-	5.033%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2015-07-06	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	225383074265950537	57.645	18	0.007	0.344	0.025

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2015-07-06

TJAOI

Manual testing

2⁵⁷

2⁵⁸*

225383074265950537

57.645

0.007

0.344

0.025

ECM factoring results:

Total ECM effort:	38.428 GHz-days
Estimated T-Level:	25.716

Digits	B1	Complete	FacMiss
20	11000	14.785	0.000%
25	50000	1.680	18.633%
30	250000	0.143	86.658%
35	1000000	0.010	99.013%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.64
250000	40000000		49	20.79

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-10-08	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-13	Gordon Spence	haswell	50000	5000000						3	0.206
2019-06-07	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-12	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-20	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-28	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-11	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-27	-Anonymous-	aws-nano	50000	5000000						3	0.206
2020-05-01	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.206
2020-05-04	TJAOI	Manual testing	50000	5000000						232	15.92
2023-07-14	TJAOI	Manual testing	250000	40000000						49	20.79

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

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