M4903631 Mersenne number exponent details

Residue

Status

L-L

92A5C413C61A7B16

double-checked

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	2⁷³	390.0873	68.4932%	1200000	39750000	0.6633	4.2959%	390.7507	69.8467%	1.3535%
PrimeNet	2⁶¹	0.0626	62.2951%	22000	450000	0.0091	3.3025%	0.0718	63.5403%	1.2452%
GPU72	2⁶⁵	1.4878	64.6154%	32000	700000	0.0137	2.3743%	1.5016	65.4555%	0.8401%
Difference	+8	+388.5995	+3.8778%	+1168000	+39050000	+0.6496	+1.9216%	+389.2491	+4.3911%	+4.3911%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

390.0873

68.4932%

1200000

39750000

0.6633

4.2959%

390.7507

69.8467%

1.3535%

PrimeNet

2⁶¹

0.0626

62.2951%

22000

450000

0.0091

3.3025%

0.0718

63.5403%

1.2452%

GPU72

2⁶⁵

1.4878

64.6154%

32000

700000

0.0137

2.3743%

1.5016

65.4555%

0.8401%

Difference

+388.5995

+3.8778%

+1168000

+39050000

+0.6496

+1.9216%

+389.2491

+4.3911%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-31T08:02:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	0.661%
2011-07-10T21:03:00	Squeeky_Squirrel	T7500_2200	60000	960000		-		-	-	0.022	-	-	1.044%
2014-09-09T05:55:00	mikr	MSI	1200000	39750000		-		-	-	0.663	-	-	4.296%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:04	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.063	-	-
2010-04-10T00:46:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.063	-	-
2011-09-03T15:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.325	-	-
2016-02-23T16:39:04	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.200	-	-
2014-12-29T19:38:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.400	-	-
2014-12-29T19:38:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.762	-	-
2015-07-24T22:13:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.524	-	-
2017-10-31T15:30:48	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	3.048	-	-
2018-05-23T15:00:47	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	6.096	-	-
2021-04-05T09:35:52	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	12.19	-	-
2021-04-23T21:07:10	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	24.38	-	-
2021-04-24T23:59:10	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	48.77	-	-
2021-04-26T20:37:09	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	97.53	-	-
2021-04-27T14:55:25	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	195.1	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.888 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.888 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.888

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-04-17T13:15:00	Csaba Vágó	debws-0364	50000	5000000						3	0.629
2014-03-09T20:09:00	zzfwind2007	zzfwind2007	50000	5000000						3	0.629
2017-05-05T12:37:13	bayanne	iMac	50000	5000000						3	0.629

date	userid	compid	res64	spent (GHz-days)
2000-04-19T00:00:00	ANONYMOUS	v4_computers	92A5C413C61A7B16	0.680

date

userid

compid

res64

spent (GHz-days)

2000-04-19T00:00:00

ANONYMOUS

v4_computers

92A5C413C61A7B16

0.680

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 = 1200000, B2 = 39750000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 60000, B2 = 960000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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