M3457123 Mersenne number exponent details

Residue

Status

L-L

0F15FBB15048A784

double-checked

PRP

C71CC22C79F00839

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	34.5336	68.1159%	5000000	200000000	2.3794	8.6502%	36.9130	70.8740%	2.7580%
PrimeNet	2⁶⁰	0.0444	63.3333%	15000	280000	0.0045	2.9024%	0.0489	64.3976%	1.0642%
GPU72	2⁶⁴	1.0296	65.6250%	19000	340000	0.0056	1.8555%	1.0351	66.2628%	0.6378%
Difference	+5	+33.5040	+2.4909%	+4981000	+199660000	+2.3738	+6.7947%	+35.8779	+4.6112%	+4.6112%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.5336

68.1159%

5000000

200000000

2.3794

8.6502%

36.9130

70.8740%

2.7580%

PrimeNet

2⁶⁰

0.0444

63.3333%

15000

280000

0.0045

2.9024%

0.0489

64.3976%

1.0642%

GPU72

2⁶⁴

1.0296

65.6250%

19000

340000

0.0056

1.8555%

1.0351

66.2628%

0.6378%

Difference

+33.5040

+2.4909%

+4981000

+199660000

+2.3738

+6.7947%

+35.8779

+4.6112%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3457123	339021860645480055543967	24	78.166	49032368915638821 3 × 10103 × 78487 × 20611687	2021-10-09	78487	20611687	33,426	0.1823	0.3194
3457123	1432323958550150534387985793	28	90.210	207155481385844607552 2⁶ × 3² × 13049 × 4525981 × 6089533	2021-10-09	4525981	6089533	81,195,406	0.7022	1.4028

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3457123

339021860645480055543967

78.166

49032368915638821
3 × 10103 × 78487 × 20611687

2021-10-09

78487

20611687

33,426

0.1823

0.3194

3457123

1432323958550150534387985793

90.210

207155481385844607552
2⁶ × 3² × 13049 × 4525981 × 6089533

2021-10-09

4525981

6089533

81,195,406

0.7022

1.4028

exponent	prime factors	composite factor	digits	bits*
3457123	339021860645480055543967 1432323958550150534387985793	48558913347477148577011475915212117674428808286083 1	51	168.376

exponent

prime factors

composite factor

digits

bits*

3457123

339021860645480055543967
1432323958550150534387985793

48558913347477148577011475915212117674428808286083
1

168.376

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-16T11:24:00	Carsten Kossendey	durandal	20000	235000		-		-	-	0.005	-	-	0.806%
2011-11-07T01:16:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.687%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78566	78566		-		-	-	0.012	-	-	0.653%
2014-09-21T23:02:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.163%
2021-10-09T21:06:31	mikr	MSI	5000000	200000000	12		339021860645480055543967 1432323958550150534387985793	51	168.376	2.379	0.726	4.759	8.650%
2022-04-10T23:56:30	Jocelyn Larouche	Manual testing	1000000	126668850		-	skipped known factor: 339021860645480055543967	-	-	1.195	-	-	6.996%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-01T00:00:00	dstrom	v4_computers	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-21T17:08:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-31T08:43:00	markr	Manual testing	2¹	2⁶²		-	-	0.178	-	-
2012-08-18T15:35:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.462	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.284	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.568	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.081	-	-
2015-04-17T22:34:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.162	-	-
2017-02-09T04:36:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.323	-	-
2019-02-04T14:28:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.646	-	-
2021-01-06T01:57:09	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.29	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.487 GHz-days
Estimated T-Level:	2.150

Digits	B1	Curves	Complete	FacMiss
20	11000	43 / 100	0.430	64.910%
25	50000	43 / 280	0.154	85.740%

New Calculation Method

Total ECM effort:	6.487 GHz-days
Estimated T-Level:	2.150

Digits	B1	Complete	FacMiss
20	11000	1.403	24.594%
25	50000	0.127	88.064%
30	250000	0.008	99.220%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.294
50000	6750000		7	1.193

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-05T12:51:00	Net_Force	Vista64	50000	5000000						3	0.441
2012-02-10T19:12:00	Piepen	T30-2200	50000	5000000						3	0.441
2015-02-27T17:48:00	Pool Party	St.P.p	50000	5000000						3	0.441
2016-12-24T19:43:59	Richard Kint	Desktop	50000	5000000						3	0.441
2019-06-11T16:01:20	penlu	pony	50000	5000000						3	0.441
2021-03-29T00:38:28	Zenzoma	AM3700X_1	50000	5000000						7	1.029
2021-05-23T18:47:09	daveward2005	d12436	50000	5000000						7	1.029
2021-06-28T05:43:23	daveward2005	Dave2	50000	5000000						7	1.029
2021-08-11T23:40:03	nordi	sweet16	50000	6750000						7	1.193

date	userid	compid	res64	spent (GHz-days)
1998-06-20T00:00:00	dstrom	v4_computers	0F15FBB15048A784	0.363
1999-07-04T00:00:00	kraDen	v4_computers	0F15FBB15048A784	0.363

date

userid

compid

res64

spent (GHz-days)

1998-06-20T00:00:00

dstrom

v4_computers

0F15FBB15048A784

0.363

1999-07-04T00:00:00

kraDen

v4_computers

0F15FBB15048A784

0.363

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 78566 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 20000 (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