M5022607 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

D799719AB1208E__

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	2⁷³	380.8469	68.4932%	560000	31360000	0.4498	3.7179%	381.2967	69.6646%	1.1714%
PrimeNet	2⁶¹	0.0612	62.2951%	22000	450000	0.0091	3.3157%	0.0703	63.5453%	1.2502%
GPU72	2⁶⁵	1.4526	64.6154%	34000	700000	0.0141	2.4178%	1.4667	65.4709%	0.8555%
Difference	+8	+379.3943	+3.8778%	+526000	+30660000	+0.4357	+1.3001%	+379.8300	+4.1936%	+4.1936%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

380.8469

68.4932%

560000

31360000

0.4498

3.7179%

381.2967

69.6646%

1.1714%

PrimeNet

2⁶¹

0.0612

62.2951%

22000

450000

0.0091

3.3157%

0.0703

63.5453%

1.2502%

GPU72

2⁶⁵

1.4526

64.6154%

34000

700000

0.0141

2.4178%

1.4667

65.4709%

0.8555%

Difference

+379.3943

+3.8778%

+526000

+30660000

+0.4357

+1.3001%

+379.8300

+4.1936%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5022607	1930601631810115754305447	25	80.675	192191189934840189 3 × 331 × 887 × 4723 × 46200073	2021-10-18	4723	46200073	88,737	0.5068	0.9449

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5022607

1930601631810115754305447

80.675

192191189934840189
3 × 331 × 887 × 4723 × 46200073

2021-10-18

4723

46200073

88,737

0.5068

0.9449

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	150000	4000000		-		-	-	0.072	-	-	1.906%
2021-04-03T00:40:16	Dylan Delgado	desktoplinux	560000	31360000		-		-	-	0.450	-	-	3.718%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-10-18T15:54:18	ATH	5960X	2500000	90000000	2	7	1930601631810115754305447	P-1	25	80.675	1.703

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:07	Mark Rose	Manual testing	2¹	2⁶³		-	-	0.318	-	-
2014-12-15T11:36:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.391	-	-
2014-12-15T11:36:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.744	-	-
2015-07-27T22:27:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.488	-	-
2016-05-15T16:59:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.976	-	-
2018-06-08T00:09:24	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.951	-	-
2021-02-01T12:43:34	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.90	-	-
2021-03-31T18:48:31	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.81	-	-
2021-03-31T18:48:31	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.61	-	-
2021-04-02T16:28:18	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	95.22	-	-
2021-04-04T19:23:31	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	190.4	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-06-27T17:40:00	James Hintz	14_052810	50000	5000000						3	0.632
2014-07-19T16:23:00	Lukasz Wrobel	w1	50000	5000000						3	0.632
2017-06-21T09:32:49	bayanne	iMac	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	41A097D750AE6D__	0.696
2000-04-05T00:00:00	kraDen	v4_computers	5806AEACBF1E40__	0.696

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 = 2500000, B2 = 90000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 560000, B2 = 31360000 (P-1 stage 2)

B1 = 560000 (P-1 stage 1)

B1 = 150000, B2 = 4000000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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