M6234523 Mersenne number exponent details

Residue

Status

L-L

4409AB22B9B218B5

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	2⁷²	153.3932	68.0556%	3000000	243000000	4.1311	7.1265%	157.5243	70.3321%	2.2765%
PrimeNet	2⁶²	0.0985	62.9032%	26000	600000	0.0147	3.3506%	0.1133	64.1462%	1.2430%
GPU72	2⁶⁶	2.3688	65.1515%	40000	900000	0.0223	2.4325%	2.3911	65.9992%	0.8477%
Difference	+6	+151.0244	+2.9040%	+2960000	+242100000	+4.1087	+4.6940%	+155.1331	+4.3329%	+4.3329%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

153.3932

68.0556%

3000000

243000000

4.1311

7.1265%

157.5243

70.3321%

2.2765%

PrimeNet

2⁶²

0.0985

62.9032%

26000

600000

0.0147

3.3506%

0.1133

64.1462%

1.2430%

GPU72

2⁶⁶

2.3688

65.1515%

40000

900000

0.0223

2.4325%

2.3911

65.9992%

0.8477%

Difference

+151.0244

+2.9040%

+2960000

+242100000

+4.1087

+4.6940%

+155.1331

+4.3329%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-04-09T00:00:00	Sturle Sunde	v4_computers	80000	1720000		-		-	-	0.044	-	-	1.567%
2013-04-21T04:53:00	Squeeky_Squirrel	P4_2600	115000	2300000		-		-	-	0.060	-	-	1.836%
2019-10-07T21:13:19	takahashi	vaio	600000	12000000	12	-		-	-	0.314	-	-	3.535%
2021-10-30T03:13:28	firejuggler	Maison	3000000	243000000		-		-	-	4.131	-	-	7.127%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.099	-	-
2016-02-23T16:39:20	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.157	-	-
2014-09-12T09:14:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.315	-	-
2014-09-17T11:17:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.599	-	-
2015-10-13T20:45:58	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.199	-	-
2016-03-21T19:29:45	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.397	-	-
2018-06-01T13:52:03	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.794	-	-
2020-04-05T23:18:51	takahashi	Manual testing	2⁶⁸	2⁶⁹		-	-	9.59	-	-
2020-07-19T02:58:34	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	19.18	-	-
2021-08-16T15:45:34	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	38.36	-	-
2021-09-21T15:11:00	SRBase	Manual testing	2⁷¹	2⁷²		-	-	76.71	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.617

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-09-27T15:14:00	JimBa	Dell	50000	5000000						3	0.808
2016-07-10T19:54:18	joe b.	Alan2012	50000	5000000						3	0.808

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	4409AB22B9B218B5	1.105
2015-11-13T16:40:44	MadPoo	Manual testing	4409AB22B9B218B5	1.105

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 = 243000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 600000, B2 = 12000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 115000, B2 = 2300000 (P-1 stage 2)

B1 = 80000, B2 = 1720000 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 80000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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