M2920531 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

54F26C660B8E473B

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	2⁶⁸	20.4089	67.6471%	1000000	20000000	0.2279	5.5374%	20.6368	69.4386%	1.7915%
PrimeNet	2⁵⁹	0.0263	62.7119%	13000	260000	0.0030	3.0682%	0.0293	63.8559%	1.1441%
GPU72	2⁶³	0.5465	65.0794%	17000	300000	0.0036	1.9440%	0.5501	65.7582%	0.6788%
Difference	+5	+19.8624	+2.5677%	+983000	+19700000	+0.2243	+3.5934%	+20.0867	+3.6804%	+3.6804%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.4089

67.6471%

1000000

20000000

0.2279

5.5374%

20.6368

69.4386%

1.7915%

PrimeNet

2⁵⁹

0.0263

62.7119%

13000

260000

0.0030

3.0682%

0.0293

63.8559%

1.1441%

GPU72

2⁶³

0.5465

65.0794%

17000

300000

0.0036

1.9440%

0.5501

65.7582%

0.6788%

Difference

+19.8624

+2.5677%

+983000

+19700000

+0.2243

+3.5934%

+20.0867

+3.6804%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2920531	129100446029146727171527	24	76.773	22102221484577073 3 × 7 × 23 × 1601 × 28582319131	2021-04-09	1601	28582319131	6,978.9	174.40	325.73

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2920531

129100446029146727171527

76.773

22102221484577073
3 × 7 × 23 × 1601 × 28582319131

2021-04-09

1601

28582319131

6,978.9

174.40

325.73

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.246%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.145%
2010-11-13T11:54:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.213%
2010-11-14T16:13:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.582%
2015-04-27T09:55:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.228	-	-	5.537%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:24	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.053	-	-
2009-02-12T23:40:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2011-12-25T18:11:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.336	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.672	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.279	-	-
2016-02-22T10:40:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.559	-	-
2017-11-22T00:30:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.117	-	-
2018-12-18T01:52:42	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.23	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.771 GHz-days
Estimated T-Level:	3.650

Digits	B1	Curves	Complete	FacMiss
20	11000	73 / 100	0.730	48.014%
25	50000	73 / 280	0.261	77.014%

New Calculation Method

Total ECM effort:	7.771 GHz-days
Estimated T-Level:	3.650

Digits	B1	Complete	FacMiss
20	11000	2.370	9.344%
25	50000	0.215	80.689%
30	250000	0.013	98.687%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	6.295
50000	5000000	129100446029146727171527	6	0.629
50000	6750000		7	0.847

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-28T02:50:00	Walt Cooney	P4	50000	5000000						3	0.315
2011-04-15T08:04:00	Smurgs	Praca	50000	5000000						3	0.315
2013-06-09T14:28:00	Richard Kint	xps	50000	5000000						3	0.315
2015-12-25T10:03:45	Bruce	Desk7	50000	5000000						3	0.315
2016-09-24T06:57:04	Bruce	test	50000	5000000						3	0.315
2019-08-03T02:07:21	S04803	lfmcal	50000	5000000						3	0.315
2020-08-21T16:43:46	mnd9	25836b	50000	5000000						7	0.734
2020-09-25T01:06:24	rextherunt	ice	50000	5000000						7	0.734
2020-10-21T20:39:29	daveward2005	Dave2	50000	5000000						7	0.734
2020-11-26T12:06:56	mnd9	libproj	50000	5000000						7	0.734
2020-12-31T09:00:57	daveward2005	Davy	50000	5000000						7	0.734
2021-01-30T23:45:09	lycorn	colab_DG	50000	6750000						7	0.847
2021-03-03T23:13:20	ZacHFX	5600X	50000	5000000						7	0.734
2021-04-09T16:23:06	daveward2005	Dave2	50000	5000000	129100446029146727171527	76.773	6	2	4850406481045220	6	0.629

date	userid	compid	res64	spent (GHz-days)
2015-11-14T06:50:02	MadPoo	Manual testing	23715C6A2F97BC__	0.226

date

userid

compid

res64

spent (GHz-days)

2015-11-14T06:50:02

MadPoo

Manual testing

23715C6A2F97BC__

0.226

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 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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