M1227649 Mersenne number exponent details

Residue

Status

L-L

121C0CECCB6FAAEE

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	24.2039	68.6567%	300000	10000000	0.0368	4.1735%	24.2408	69.9648%	1.3081%
PrimeNet	2⁵⁶	0.0078	62.5000%	5500	90000	0.0004	2.4275%	0.0083	63.4103%	0.9103%
GPU72	2⁶⁰	0.1251	65.0000%	5000	30000	0.0003	0.8301%	0.1254	65.2905%	0.2905%
Difference	+7	+24.0788	+3.6567%	+295000	+9970000	+0.0366	+3.3433%	+24.1154	+4.6743%	+4.6743%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

24.2039

68.6567%

300000

10000000

0.0368

4.1735%

24.2408

69.9648%

1.3081%

PrimeNet

2⁵⁶

0.0078

62.5000%

5500

90000

0.0004

2.4275%

0.0083

63.4103%

0.9103%

GPU72

2⁶⁰

0.1251

65.0000%

5000

30000

0.0003

0.8301%

0.1254

65.2905%

0.2905%

Difference

+24.0788

+3.6567%

+295000

+9970000

+0.0366

+3.3433%

+24.1154

+4.6743%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1227649	15416236911951515369	20	63.741	6278764089716 2² × 691 × 2271622319	2009-10-07	691	2271622319	1.7141	5.5034	10.279

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1227649

15416236911951515369

63.741

6278764089716
2² × 691 × 2271622319

2009-10-07

691

2271622319

1.7141

5.5034

10.279

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-09-22T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.005%
2002-12-09T00:00:00	ANONYMOUS	v4_computers	20000	395000		-		-	-	0.002	-	-	1.039%
2016-03-17T19:02:32	alpertron	Manual testing	300000	10000000	12	-		-	-	0.037	-	-	4.173%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2022-03-07T17:31:40	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.094	-	-
2009-02-15T05:34:00	Sturle Sunde	golan.ifi	2⁶⁰	2⁶¹		-	-	0.125	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.645 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	19.645 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	15.092	0.000%
25	50000	1.656	19.090%
30	250000	0.137	87.221%
35	1000000	0.009	99.079%

ECM Summary

B1	B2	factor	curves	GHz-days
		15416236911951515369	1	0.00000e+0
50000	5000000		278	10.29
250000	35000000		44	9.359

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-05T09:12:00	Andi47	Core2Duo	50000	5000000						1	0.037
2008-08-17T18:30:00	Sturle Sunde	v21	50000	5000000						3	0.111
2009-01-25T15:35:00	Sturle Sunde	v23	50000	5000000						3	0.111
2009-06-26T05:03:00	SubPrime	c2d0	50000	5000000						3	0.111
2009-10-07T15:31:00	SubPrime	c2d0			15416236911951515369	63.741		1		1	-
2017-11-03T14:25:25	TJAOI	Manual testing	50000	5000000						127	4.699
2018-10-05T13:06:59	TJAOI	Manual testing	50000	5000000						141	5.217
2021-04-16T16:22:17	TJAOI	Manual testing	250000	35000000						44	9.359

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 20000, B2 = 395000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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