M1527607 Mersenne number exponent details

Residue

Status

L-L

5F8E824BB4F2FF43

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	19.4513	68.6567%	500000	15000000	0.0835	4.9593%	19.5348	70.2111%	1.5544%
PrimeNet	2⁵⁷	0.0126	63.1579%	6500	110000	0.0008	2.4135%	0.0134	64.0471%	0.8892%
GPU72	2⁶¹	0.2011	65.5738%	6500	55000	0.0006	1.0138%	0.2017	65.9228%	0.3490%
Difference	+6	+19.2502	+3.0829%	+493500	+14945000	+0.0830	+3.9455%	+19.3332	+4.2883%	+4.2883%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.4513

68.6567%

500000

15000000

0.0835

4.9593%

19.5348

70.2111%

1.5544%

PrimeNet

2⁵⁷

0.0126

63.1579%

6500

110000

0.0008

2.4135%

0.0134

64.0471%

0.8892%

GPU72

2⁶¹

0.2011

65.5738%

6500

55000

0.0006

1.0138%

0.2017

65.9228%

0.3490%

Difference

+19.2502

+3.0829%

+493500

+14945000

+0.0830

+3.9455%

+19.3332

+4.2883%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1527607	56798545755513540071	20	65.622	18590693076005 5 × 3718138615201	2013-08-20	5	3718138615201	6.0518	13,120	24,505

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1527607

56798545755513540071

65.622

18590693076005
5 × 3718138615201

2013-08-20

3718138615201

6.0518

13,120

24,505

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	285000		-		-	-	0.002	-	-	0.985%
2011-01-30T21:51:00	James Heinrich	WHS	80000	1340000		-		-	-	0.010	-	-	2.193%
2016-03-17T19:15:55	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	4.959%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.025	-	-
2010-04-25T20:40:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.101	-	-
2010-05-04T02:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.045	-	-
2011-05-07T06:36:00	Xyzzy	Manual testing	2⁶³	2⁶⁴		-	-	1.285	-	-
2011-05-07T06:36:00	Xyzzy	Manual testing	2⁶⁴	2⁶⁵		-	-	2.446	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.897 GHz-days
Estimated T-Level:	24.446

Digits	B1	Curves	Complete	FacMiss
20	11000	249 / 100	2.490	8.188%
25	50000	249 / 280	0.889	41.030%

New Calculation Method

Total ECM effort:	13.897 GHz-days
Estimated T-Level:	24.446

Digits	B1	Complete	FacMiss
20	11000	8.032	0.032%
25	50000	0.726	48.387%
30	250000	0.045	95.628%
35	1000000	0.002	99.796%

ECM Summary

B1	B2	factor	curves	GHz-days
		56798545755513540071	1	0.00000e+0
50000	5000000		249	13.90

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-23T02:36:00	Steve Scott	Printer	50000	5000000						3	0.167
2009-04-11T02:18:00	Adel El-Atawy	SRVRARC	50000	5000000						3	0.167
2010-02-08T23:19:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.167
2011-04-17T05:33:00	Beat Bucheli	I7	50000	5000000						3	0.167
2012-10-29T05:46:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.167
2013-08-20T08:44:00	Chang Chia-Tche	exbpc13			56798545755513540071	65.622		1		1	-
2019-06-07T09:14:59	TJAOI	Manual testing	50000	5000000						234	13.06

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	5F8E824BB4F2FF43	0.068

date

userid

compid

res64

spent (GHz-days)

1999-02-14T00:00:00

ANONYMOUS

v4_computers

5F8E824BB4F2FF43

0.068

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 80000, B2 = 1340000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 20000, B2 = 285000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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