M5007881 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

82B68F768ABABCC8

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	381.9668	68.4932%	3600000	120000000	1.9982	5.8485%	383.9650	70.3358%	1.8427%
PrimeNet	2⁶¹	0.0613	62.2951%	22000	450000	0.0091	3.3141%	0.0704	63.5447%	1.2496%
GPU72	2⁶⁵	1.4568	64.6154%	34000	700000	0.0141	2.4167%	1.4710	65.4705%	0.8551%
Difference	+8	+380.5100	+3.8778%	+3566000	+119300000	+1.9840	+3.4319%	+382.4940	+4.8653%	+4.8653%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

381.9668

68.4932%

3600000

120000000

1.9982

5.8485%

383.9650

70.3358%

1.8427%

PrimeNet

2⁶¹

0.0613

62.2951%

22000

450000

0.0091

3.3141%

0.0704

63.5447%

1.2496%

GPU72

2⁶⁵

1.4568

64.6154%

34000

700000

0.0141

2.4167%

1.4710

65.4705%

0.8551%

Difference

+380.5100

+3.8778%

+3566000

+119300000

+1.9840

+3.4319%

+382.4940

+4.8653%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5007881	204601013221187093861783	24	77.437	20427902861628211 569 × 821 × 43728880639	2021-10-17	821	43728880639	8,693.1	478.84	894.35

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5007881

204601013221187093861783

77.437

20427902861628211
569 × 821 × 43728880639

2021-10-17

821

43728880639

8,693.1

478.84

894.35

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.006%
2009-07-13T19:54:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.005%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	67817	67817		-		-	-	0.014	-	-	0.348%
2016-12-02T21:10:01	Squeeky_Squirrel	i5-5250U_1600	300000	9375000	12	-		-	-	0.160	-	-	2.644%
2018-07-09T06:28:29	mikr	S054	3600000	120000000	12	-		-	-	1.998	-	-	5.849%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-10-17T23:45:04	ATH	ec2-P_1	2500000	2500000	2	7	204601013221187093861783	P+1	24	77.437	0.844

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:06	Mark Rose	Manual testing	2¹	2⁶³		-	-	0.319	-	-
2014-08-26T01:15:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.392	-	-
2014-08-29T00:05:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.746	-	-
2015-07-23T03:14:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.492	-	-
2016-05-14T03:02:04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.984	-	-
2017-10-22T18:44:16	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	5.969	-	-
2021-02-23T10:39:17	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.94	-	-
2021-04-01T10:42:20	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.88	-	-
2021-04-01T10:42:20	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.75	-	-
2021-04-03T10:35:53	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	95.50	-	-
2021-04-04T19:23:42	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	191.0	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.593 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	3.593 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.532	58.760%
25	50000	0.048	95.303%
30	250000	0.003	99.703%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897
50000	6500000		7	1.696

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-06-25T16:16:00	ANONYMOUS	mosura99	50000	5000000						3	0.632
2014-05-08T19:14:00	S00030	op9020-usff	50000	5000000						3	0.632
2017-06-12T23:26:25	Bruce	Desk10	50000	5000000						3	0.632
2021-01-23T09:57:24	George Woltman	x64-debug	50000	6500000						7	1.696

date	userid	compid	res64	spent (GHz-days)
2000-07-12T00:00:00	arnaud	v4_computers	69D37DFC6B2835__	0.694

date

userid

compid

res64

spent (GHz-days)

2000-07-12T00:00:00

arnaud

v4_computers

69D37DFC6B2835__

0.694

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 = 3600000, B2 = 120000000 (P-1 stage 2)

B1 = 3600000 (P-1 stage 1)

B1 = 2500000 (P+1 stage 1)

B1 = 300000, B2 = 9375000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 67817 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

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