M4676593 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	6.3538	65.6716%	-	-	-	-	6.3538	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0657	62.2951%	20000	400000	0.0078	3.1193%	0.0735	63.4712%	1.1761%
GPU72	2⁶⁵	1.5600	64.6154%	30000	600000	0.0117	2.2308%	1.5717	65.4047%	0.7894%
Difference	+2	+4.7937	+1.0563%	-30000	-600000	-0.0117	-2.2308%	+4.7821	+0.2669%	+0.2669%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.3538

65.6716%

6.3538

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0657

62.2951%

20000

400000

0.0078

3.1193%

0.0735

63.4712%

1.1761%

GPU72

2⁶⁵

1.5600

64.6154%

30000

600000

0.0117

2.2308%

1.5717

65.4047%

0.7894%

Difference

+4.7937

+1.0563%

-30000

-600000

-0.0117

-2.2308%

+4.7821

+0.2669%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4676593	102885047	9	26.616	11 11	-	1	11	1.916e-12	2.949e-7	3.885e-7
4676593	1683788603279	13	40.615	180023 180023	2008-09-07	1	180023	6.158e-8	0.0019	0.0035
4676593	123377477734208519	18	56.776	13190957363 13190957363	2015-04-29	1	13190957363	0.0032	137.21	256.27
4676593	104935168370529292206977	24	76.474	11219189736046016 2⁶ × 175299839625719	2019-03-26	64	175299839625719	3,949.6	1,823,410	3,405,623

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4676593

102885047

26.616

11
11

1.916e-12

2.949e-7

3.885e-7

4676593

1683788603279

40.615

180023
180023

2008-09-07

180023

6.158e-8

0.0019

0.0035

4676593

123377477734208519

56.776

13190957363
13190957363

2015-04-29

13190957363

0.0032

137.21

256.27

4676593

104935168370529292206977

76.474

11219189736046016
2⁶ × 175299839625719

2019-03-26

175299839625719

3,949.6

1,823,410

3,405,623

exponent	prime factors	composite factor	digits	bits*
4676593	102885047 1683788603279	173236669586424269113	21	67.231
4676593	102885047 123377477734208519	12693697595425496985115393	26	83.392
4676593	1683788603279 123377477734208519	207741590910168883805553133801	30	97.391
4676593	102885047 104935168370529292206977	10796259729754819643591562372919	32	103.090
4676593	1683788603279 104935168370529292206977	176688640585460215271142262208877583	36	117.089
4676593	102885047 1683788603279 123377477734208519	21373503344647498388271873032113173647	38	124.007
4676593	123377477734208519 104935168370529292206977	12946636399170399787434538934431824637063	41	133.250
4676593	102885047 1683788603279 104935168370529292206977	18178619091001181764801589391046693944201401	44	143.705
4676593	102885047 123377477734208519 104935168370529292206977	1332015294420557343138992547692348196079984696961	49	159.866
4676593	1683788603279 123377477734208519 104935168370529292206977	21799398819720189372404440807050306967087769866729 577	53	173.865
4676593	102885047 1683788603279 123377477734208519 104935168370529292206977	22428321721386562104287313954420887636732526558636 56265935119	61	200.481

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07T23:42:00	Will Edgington	Manual testing	?	?	1683788603279	40.615	13	3.02565e-8	1.318	6.47531e-8
2015-04-29T11:50:00	TJAOI	Manual testing	2⁵⁶	2⁵⁷*	123377477734208519	56.776	18	0.001	1.314	0.003

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.591 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.591 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	104935168370529292206977	3	0.591

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-03-27T02:10:44	ATH	ec2-ECMCF	50000	5000000	104935168370529292206977	76.474	3	2	7864889710492573	3	0.591

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-18T06:54:53

kkmrkkblmbrbk

c4.xlarge

102885047

1683788603279

123377477734208519

67BDBDFCE2C8AC__

2018-03-07T23:10:34

Oliver Kruse

GTX-5

102885047

1683788603279

123377477734208519

67BDBDFCE2C8AC__

2019-03-27T19:09:13

artorollo

fourth

102885047

1683788603279

123377477734208519

104935168370529292206977

67BDBDFCE2C8ACF7

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

10⁰

10¹

10²

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