M700079 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	unknown	1000000000	1005795841050	1,614.3322	68.7308%	1,614.3322	68.7308%	68.7308%
PrimeNet	2⁴⁰	0.0000	50.0000%	6500	260000	0.0006	21.4739%	0.0006	60.7369%	10.7369%
GPU72	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5002%	0.0010	62.0456%	7.5001%
Difference	-44	0.0000	-54.5455%	+999988000	+1005795391050	+1,614.3311	+52.2306%	+1,614.3311	+6.6852%	+6.6852%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

1000000000

1005795841050

1,614.3322

68.7308%

1,614.3322

68.7308%

PrimeNet

2⁴⁰

0.0000

50.0000%

6500

260000

0.0006

21.4739%

0.0006

60.7369%

10.7369%

GPU72

2⁴⁴

0.0000

54.5455%

12000

450000

0.0010

16.5002%

0.0010

62.0456%

7.5001%

Difference

-44

0.0000

-54.5455%

+999988000

+1005795391050

+1,614.3311

+52.2306%

+1,614.3311

+6.6852%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
700079	1400159	7	20.417	1 1	-	1	1	1.996e-13	2.896e-8	5.894e-8
700079	3556461058261458812330089494359	31	101.488	2540042665371664349544901 11² × 577 × 36381435257482623853	2020-08-25	577	36381435257482623853	2.251e+11	5.740e+10	1.072e+11

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

700079

1400159

20.417

1
1

1.996e-13

2.896e-8

5.894e-8

700079

3556461058261458812330089494359

101.488

2540042665371664349544901
11² × 577 × 36381435257482623853

2020-08-25

577

36381435257482623853

2.251e+11

5.740e+10

1.072e+11

exponent	prime factors	composite factor	digits	bits*
700079	1400159 3556461058261458812330089494359	4979610958874305909213285776332203081	37	121.905

exponent

prime factors

composite factor

digits

bits*

700079

1400159
3556461058261458812330089494359

4979610958874305909213285776332203081

121.905

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T18:50:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1400159	-	-	0.037	-	-	29.419%
2022-01-11T21:45:45	Seth_Tr	Manual testing	1000000000	1005795841050		-	skipped known factor: 1400159	-	-	1,614	-	-	61.044%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.909 GHz-days
Estimated T-Level:	25.594

Digits	B1	Curves	Complete	FacMiss
20	11000	357 / 100	3.570	2.765%
25	50000	357 / 280	1.275	27.879%
30	250000	76 / 640	0.119	88.795%

New Calculation Method

Total ECM effort:	14.909 GHz-days
Estimated T-Level:	25.594

Digits	B1	Complete	FacMiss
20	11000	15.398	0.000%
25	50000	1.735	17.642%
30	250000	0.149	86.133%
35	1000000	0.011	98.952%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	6.338
250000	25000000		44	4.962
250000	25000000	3556461058261458812330089494359	32	3.609

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-09-25T10:26:04	TJAOI	Manual testing	50000	5000000						100	2.256
2016-05-06T13:26:08	TJAOI	Manual testing	50000	5000000						90	2.030
2017-02-10T18:29:00	TJAOI	Manual testing	50000	5000000						91	2.053
2018-10-12T13:38:25	TJAOI	Manual testing	250000	25000000						44	4.962
2020-08-25T03:36:23	nordi	sweet16	250000	25000000	3556461058261458812330089494359	101.488	32	2	1274363772300438	32	3.609

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T15:51:04

Oliver Kruse

GTX-3

1400159

658BE5BE81C81A__

2017-09-28T09:45:30

Oliver Kruse

Manual testing

1400159

658BE5BE81C81A__

2017-11-08T20:18:28

kkmrkkblmbrbk

c4.large

1400159

658BE5BE81C81A__

2020-04-20T07:05:43

Oliver Kruse

AddPrpType5

1400159

F02159F54C15FA__

2020-08-25T04:31:51

CrypticClue

cruncher

1400159

3556461058261458812330089494359

F02159F54C15FA35

2020-08-25T12:06:57

ANONYMOUS

dory

1400159

3556461058261458812330089494359

F02159F54C15FA35

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 = 1000000000, B2 = 1005795841050 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

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