M457 789 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	unknown	3000000	100000000	0.1415	34.8396%	0.1415	34.8396%
Target	2⁴⁴	0.0000	56.8182%	8000	2080000	0.0021	13.8678%	0.0021	62.8066%
Difference	-44	0.0000	-56.8182%	+2992000	+97920000	+0.1394	+20.9718%	+0.1394	-27.9669%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

3000000

100000000

0.1415

34.8396%

0.1415

34.8396%

Target

2⁴⁴

0.0000

56.8182%

8000

2080000

0.0021

13.8678%

0.0021

62.8066%

Difference

-44

0.0000

-56.8182%

+2992000

+97920000

+0.1394

+20.9718%

+0.1394

-27.9669%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
457789	3072836331839	13	41.483	3356171 7 × 13² × 2837	-	169	2837	9.240e-7	5.369e-6	5.874e-6
457789	1193136663599251577	19	60.049	1303151302892 2² × 2917 × 111685919	2015-04-17	2917	111685919	0.5295	0.1040	0.1941
457789	6849713945046650946278287	25	82.502	7481300277034453587 3 × 151 × 563 × 641 × 45762786413	2020-05-18	641	45762786413	3,791,466	42.580	79.527

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

457789

3072836331839

41.483

3356171
7 × 13² × 2837

169

2837

9.240e-7

5.369e-6

5.874e-6

457789

1193136663599251577

60.049

1303151302892
2² × 2917 × 111685919

2015-04-17

2917

111685919

0.5295

0.1040

0.1941

457789

6849713945046650946278287

82.502

7481300277034453587
3 × 151 × 563 × 641 × 45762786413

2020-05-18

641

45762786413

3,791,466

42.580

79.527

exponent	prime factors	composite factor	digits	bits*
457789	3072836331839 1193136663599251577	3666313688756947130974416060103	31	101.532
457789	3072836331839 6849713945046650946278287	21048049873043596517493589673972479793	38	123.985
457789	1193136663599251577 6849713945046650946278287	8172644843002228372936364538662086765608599	43	142.552
457789	3072836331839 1193136663599251577 6849713945046650946278287	25113200000793887481596747710354524193573875129555 883561	56	184.034

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17	alpertron	Manual testing	3000000	100000000	12	-	skipped known factor: 3072836331839	-	-	0.141	-	-	34.840%

ECM factoring results:

Total ECM effort:	12.906 GHz-days
Estimated T-Level:	26.435

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		277	3.571
50000	5000000	1193136663599251577	4	0.052
250000	25000000		55	3.546
250000	25000000	6849713945046650946278287	89	5.738

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-02-01	Richard B. Woods	Puttputt	50000	5000000						1	0.013
2015-04-17	TJAOI	Manual testing	50000	5000000						95	1.225
2015-04-17	TJAOI	Manual testing	50000	5000000	1193136663599251577	60.049	4	2		4	0.052
2016-02-12	TJAOI	Manual testing	50000	5000000						90	1.160
2016-06-24	TJAOI	Manual testing	50000	5000000						91	1.173
2018-03-09	TJAOI	Manual testing	250000	25000000						44	2.837
2020-05-18	TJAOI	Manual testing	250000	25000000	6849713945046650946278287	82.502	89	2		89	5.738
2020-05-18	TJAOI	Manual testing	250000	25000000						11	0.709

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-25

Oliver Kruse

Doppelherz

3072836331839

1193136663599251577

D6A6FC35B0B374__

2017-09-27

Oliver Kruse

Manual testing

3072836331839

1193136663599251577

D6A6FC35B0B374__

2017-11-07

kkmrkkblmbrbk

c4.xlarge

3072836331839

1193136663599251577

D6A6FC35B0B374__

2020-04-18

Oliver Kruse

AddPrpType5

3072836331839

1193136663599251577

12ACE766BE1802__

2020-05-18

CrypticClue

cruncher

3072836331839

1193136663599251577

6849713945046650946278287

12ACE766BE18021A

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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