M2225627 Mersenne number exponent details

Residue

Status

L-L

93FDBF7DA5FEEF8B

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	13.3508	67.1642%	500000	15000000	0.1230	5.1893%	13.4738	68.8681%	1.7039%
PrimeNet	2⁵⁸	0.0173	62.0690%	10000	180000	0.0018	2.8692%	0.0191	63.1573%	1.0883%
GPU72	2⁶²	0.2760	64.5161%	11000	180000	0.0019	1.6307%	0.2780	65.0948%	0.5786%
Difference	+5	+13.0748	+2.6481%	+489000	+14820000	+0.1211	+3.5586%	+13.1958	+3.7733%	+3.7733%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.3508

67.1642%

500000

15000000

0.1230

5.1893%

13.4738

68.8681%

1.7039%

PrimeNet

2⁵⁸

0.0173

62.0690%

10000

180000

0.0018

2.8692%

0.0191

63.1573%

1.0883%

GPU72

2⁶²

0.2760

64.5161%

11000

180000

0.0019

1.6307%

0.2780

65.0948%

0.5786%

Difference

+13.0748

+2.6481%

+489000

+14820000

+0.1211

+3.5586%

+13.1958

+3.7733%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2225627	4421699604687113629663	22	71.905	993360433865853 3 × 349 × 47309 × 20054711	2013-06-15	47309	20054711	288.90	0.1084	0.1946

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2225627

4421699604687113629663

71.905

993360433865853
3 × 349 × 47309 × 20054711

2013-06-15

47309

20054711

288.90

0.1084

0.1946

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.281%
2010-10-21T22:29:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.782%
2011-01-13T00:05:00	Oscar Östlin		85000	1593750		-		-	-	0.016	-	-	2.458%
2016-04-05T11:23:21	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.189%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2022-03-09T16:36:28	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.069	-	-
2009-01-11T12:27:00	Sturle Sunde	jodel.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-19T18:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.772 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:	0.772 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
		4421699604687113629663	1	0.00000e+0
50000	5000000		9	0.772

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-15T17:23:00	Nathan Slaven	q6600	50000	5000000						3	0.257
2009-12-20T14:48:00	James Hintz	ryan	50000	5000000						3	0.257
2011-09-28T17:17:00	S36049	Wolle5	50000	5000000						3	0.257
2013-06-15T04:52:00	Xyzzy	J			4421699604687113629663	71.905		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	93FDBF7DA5FEEF8B	0.146

date

userid

compid

res64

spent (GHz-days)

1999-02-21T00:00:00

ANONYMOUS

v4_computers

93FDBF7DA5FEEF8B

0.146

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T20:57:33

Oliver Kruse

GTX-2

4421699604687113629663

9932970847301C__

2017-11-20T09:58:43

kkmrkkblmbrbk

c4.xlarge

4421699604687113629663

9932970847301C__

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 = 85000, B2 = 1593750 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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