M4764203 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	6.2369	65.6716%	-	-	-	-	6.2369	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0645	62.2951%	20000	450000	0.0083	3.2206%	0.0728	63.5094%	1.2143%
GPU72	2⁶⁵	1.5314	64.6154%	30000	650000	0.0122	2.2838%	1.5435	65.4235%	0.8081%
Difference	+2	+4.7056	+1.0563%	-30000	-650000	-0.0122	-2.2838%	+4.6934	+0.2482%	+0.2482%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.2369

65.6716%

6.2369

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0645

62.2951%

20000

450000

0.0083

3.2206%

0.0728

63.5094%

1.2143%

GPU72

2⁶⁵

1.5314

64.6154%

30000

650000

0.0122

2.2838%

1.5435

65.4235%

0.8081%

Difference

+4.7056

+1.0563%

-30000

-650000

-0.0122

-2.2838%

+4.6934

+0.2482%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4764203	123869279	9	26.884	13 13	-	1	13	1.882e-12	3.157e-7	3.885e-7
4764203	3681633152311	13	41.743	386385 3 × 5 × 25759	2008-09-30	5	25759	1.004e-7	0.0003	0.0005
4764203	726742410842429183	18	59.334	76271142397 29 × 163 × 3533 × 4567	2015-11-12	3533	4567	0.0206	0.0007	0.0014
4764203	78217557415660256887	20	66.084	8208881676081 3² × 6701 × 7687 × 17707	2019-05-12	7687	17707	4.9882	0.0016	0.0030

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4764203

123869279

26.884

13
13

1.882e-12

3.157e-7

3.885e-7

4764203

3681633152311

41.743

386385
3 × 5 × 25759

2008-09-30

25759

1.004e-7

0.0003

0.0005

4764203

726742410842429183

59.334

76271142397
29 × 163 × 3533 × 4567

2015-11-12

3533

4567

0.0206

0.0007

0.0014

4764203

78217557415660256887

66.084

8208881676081
3² × 6701 × 7687 × 17707

2019-05-12

7687

17707

4.9882

0.0016

0.0030

exponent	prime factors	composite factor	digits	bits*
4764203	123869279 3681633152311	456041244119260753769	21	68.628
4764203	123869279 726742410842429183	90021058449773485506769057	26	86.218
4764203	123869279 78217557415660256887	9688752442218939329547474473	28	92.968
4764203	3681633152311 726742410842429183	2675598952947908418117070291913	31	101.078
4764203	3681633152311 78217557415660256887	287968352474283906080285857715857	33	107.828
4764203	726742410842429183 78217557415660256887	56844016246463059821207739284885533321	38	125.418
4764203	123869279 3681633152311 726742410842429183	331424513194812340310192034651582840727	39	127.962
4764203	123869279 3681633152311 78217557415660256887	35670432195807413487468725309159793457103	41	134.712
4764203	123869279 726742410842429183 78217557415660256887	7041227307913665520186871574438746610002745559	46	152.303
4764203	3681633152311 726742410842429183 78217557415660256887	20927881472348349283376761723460295891739365865483 1	51	167.162
4764203	123869279 3681633152311 726742410842429183 78217557415660256887	25923215889772484625720461600398242372364173056746 025836849	59	194.046

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T21:36:00	markr	Manual testing	?	?	3681633152311	41.743	13	3.89302e-8	1.340	8.31408e-8
2015-11-12T11:43:39	TJAOI	Manual testing	2⁵⁹	2⁶⁰*	726742410842429183	59.334	18	0.005	1.307	0.009

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.593 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:	0.593 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	78217557415660256887	3	0.593

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-05-12T21:47:29	MarkS	laptop64	50000	5000000	78217557415660256887	66.084	3	2		3	0.593

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-20T03:01:34

Oliver Kruse

GTX-1

123869279

3681633152311

726742410842429183

AB942DA93143FE__

2018-01-05T17:39:20

kkmrkkblmbrbk

c4.xlarge

123869279

3681633152311

726742410842429183

AB942DA93143FE__

2019-05-13T19:06:08

artorollo

fourth

123869279

3681633152311

726742410842429183

78217557415660256887

AB942DA93143FE96

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

10³

10⁴

10⁰

10¹

10²

10³

10⁴

10⁵

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