M3450593 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

34F88A050D1299F4

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	34.5989	68.1159%	1000000	126668850	1.1950	6.9947%	35.7939	70.3462%	2.2302%
PrimeNet	2⁶⁰	0.0445	63.3333%	15000	280000	0.0045	2.9015%	0.0490	64.3972%	1.0639%
GPU72	2⁶⁴	1.0315	65.6250%	19000	340000	0.0056	1.8548%	1.0371	66.2626%	0.6376%
Difference	+5	+33.5674	+2.4909%	+981000	+126328850	+1.1894	+5.1399%	+34.7568	+4.0836%	+4.0836%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.5989

68.1159%

1000000

126668850

1.1950

6.9947%

35.7939

70.3462%

2.2302%

PrimeNet

2⁶⁰

0.0445

63.3333%

15000

280000

0.0045

2.9015%

0.0490

64.3972%

1.0639%

GPU72

2⁶⁴

1.0315

65.6250%

19000

340000

0.0056

1.8548%

1.0371

66.2626%

0.6376%

Difference

+33.5674

+2.4909%

+981000

+126328850

+1.1894

+5.1399%

+34.7568

+4.0836%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3450593	373169996182993917098039	24	78.304	54073313801858683 54073313801858683	2021-06-24	1	54073313801858683	31,730	448,656,799	837,965,958

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3450593

373169996182993917098039

78.304

54073313801858683
54073313801858683

2021-06-24

54073313801858683

31,730

448,656,799

837,965,958

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-15T21:08:00	Carsten Kossendey	durandal	20000	235000		-		-	-	0.005	-	-	0.805%
2011-11-05T07:42:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.665%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78601	78601		-		-	-	0.012	-	-	0.653%
2014-09-20T06:26:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.162%
2022-04-10T23:56:41	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.995%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-22T09:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-07-31T08:41:00	markr	Manual testing	2¹	2⁶²		-	-	0.178	-	-
2012-08-18T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.463	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.284	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.569	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.083	-	-
2015-04-16T22:33:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.166	-	-
2017-02-09T04:36:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.331	-	-
2019-02-18T10:31:22	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.663	-	-
2021-01-05T01:49:28	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.33	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.406 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	4.406 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	1.157	31.441%
25	50000	0.107	89.886%
30	250000	0.007	99.330%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4700000		7	1.001
50000	5000000		22	3.234
50000	6800000	373169996182993917098039	1	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-01T09:28:00	sasaki3	ssk_saver	50000	5000000						3	0.441
2012-02-06T06:19:00	Piepen	T30-2200	50000	5000000						3	0.441
2015-02-09T07:54:00	NeoGen	DC-CPU2	50000	5000000						3	0.441
2016-12-18T06:13:03	NBCC	wed_a8c	50000	5000000						3	0.441
2019-06-05T19:58:39	IanGlencross	glenx24	50000	5000000						3	0.441
2021-03-29T06:18:07	debrouxl	Manual testing	50000	5000000						7	1.029
2021-05-13T01:36:18	kutens	capella	50000	4700000						7	1.001
2021-06-24T12:46:26	kutens	canopus	50000	6800000	373169996182993917098039	78.304	1	2	5949249494599290	1	0.171

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	4D13B982F0C410__	0.362

date

userid

compid

res64

spent (GHz-days)

1999-07-27T00:00:00

ANONYMOUS

v4_computers

4D13B982F0C410__

0.362

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 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 78601 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 235000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

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10³

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10¹⁷

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