M423289 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	70.1977	71.6418%	3000000	100000000	0.1165	7.1562%	70.3142	73.6712%	2.0294%
PrimeNet	2⁴⁰	0.0000	52.5000%	4000	140000	0.0002	17.8508%	0.0002	60.9791%	8.4791%
GPU72	2⁴⁴	0.0000	56.8182%	7000	220000	0.0003	13.1619%	0.0003	62.5017%	5.6835%
Difference	+23	+70.1977	+14.8236%	+2993000	+99780000	+0.1162	-6.0056%	+70.3139	+11.1695%	+11.1695%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
423289	3093317790813753846743	22	71.390	3653907603095939 7 × 23 × 18859 × 1203408361	2008-01-12	18859	1203408361	1,364.0	0.9219	1.7214

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-01T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.001	-	-	1.466%
2002-06-15T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.003	-	-	1.707%
2002-08-24T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.006	-	-	2.430%
2003-03-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.012	-	-	3.281%
2016-03-17T18:47:52	alpertron	Manual testing	3000000	100000000	12	-		-	-	0.116	-	-	7.156%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-03-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.023	-	-
2002-01-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.045	-	-
2004-01-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.091	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.512 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	419 / 100	4.190	1.483%
25	50000	419 / 280	1.496	22.333%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	10.512 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.668	0.000%
25	50000	3.007	4.945%
30	250000	0.286	75.150%
35	1000000	0.022	97.838%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		3093317790813753846743	1	0.00000e+0
50000	5000000		275	2.905
250000	25000000		144	7.607

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-15T01:18:00	Team_Bundu	bundu1	50000	5000000						1	0.011
2007-09-02T16:38:00	Chad Davis	Bayes	50000	5000000						1	0.011
2007-10-15T20:14:00	ANONYMOUS	minister	50000	5000000						1	0.011
2008-01-12T00:18:00	Team_Bundu	bundu2			3093317790813753846743	71.390		1		1	-
2013-10-20T18:59:00	Richard B. Woods	Puttputt	50000	5000000						3	0.032
2013-10-20T20:25:00	Richard B. Woods	Puttputt	50000	5000000						2	0.021
2014-11-21T11:34:00	TJAOI	Manual testing	50000	5000000						36	0.380
2015-04-03T14:24:00	TJAOI	Manual testing	50000	5000000						50	0.528
2016-01-29T11:38:48	TJAOI	Manual testing	50000	5000000						90	0.951
2016-10-14T16:20:18	TJAOI	Manual testing	50000	5000000						91	0.961
2018-03-09T17:07:06	TJAOI	Manual testing	250000	25000000						44	2.324
2020-08-28T11:11:09	TJAOI	Manual testing	250000	25000000						100	5.283

date	userid	compid	res64	spent (GHz-days)
2002-02-03T00:00:00	ANONYMOUS	v4_computers	E6916CC99F3409__	0.004

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-23T13:22:05

Oliver Kruse

Doppelherz

3093317790813753846743

47EF37ED341BD4__

2017-09-24T17:46:56

Oliver Kruse

Manual testing

3093317790813753846743

47EF37ED341BD4__

2017-11-07T01:18:58

kkmrkkblmbrbk

c4.xlarge

3093317790813753846743

47EF37ED341BD4__

2020-04-18T17:31:55

Oliver Kruse

AddPrpType5

3093317790813753846743

BEF10707EFC026__

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 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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