M1321171 Mersenne number exponent details

Residue

Status

L-L

7DC38B2880BC9FF4

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	22.4906	68.6567%	500000	15000000	0.0593	4.8729%	22.5499	70.1840%	1.5273%
PrimeNet	2⁵⁶	0.0073	62.5000%	6000	100000	0.0005	2.6019%	0.0078	63.4757%	0.9757%
GPU72	2⁶⁰	0.1163	65.0000%	5500	40000	0.0003	0.9768%	0.1166	65.3419%	0.3419%
Difference	+7	+22.3743	+3.6567%	+494500	+14960000	+0.0589	+3.8961%	+22.4333	+4.8422%	+4.8422%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.4906

68.6567%

500000

15000000

0.0593

4.8729%

22.5499

70.1840%

1.5273%

PrimeNet

2⁵⁶

0.0073

62.5000%

6000

100000

0.0005

2.6019%

0.0078

63.4757%

0.9757%

GPU72

2⁶⁰

0.1163

65.0000%

5500

40000

0.0003

0.9768%

0.1166

65.3419%

0.3419%

Difference

+22.3743

+3.6567%

+494500

+14960000

+0.0589

+3.8961%

+22.4333

+4.8422%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1321171	8399774438446404972583	22	72.831	3178912660982721 3³ × 13 × 9056731227871	2014-03-09	27	9056731227871	755.35	22,677	42,354

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1321171

8399774438446404972583

72.831

3178912660982721
3³ × 13 × 9056731227871

2014-03-09

9056731227871

755.35

22,677

42,354

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.001	-	-	0.794%
2012-11-03T06:31:00	kurly	smile	500000	10000000		-		-	-	0.047	-	-	4.503%
2016-03-17T19:04:56	alpertron	Manual testing	500000	15000000	12	-		-	-	0.059	-	-	4.873%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.029	-	-
2022-03-07T17:32:33	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.087	-	-
2009-02-14T23:41:00	Sturle Sunde	rodolfo.ifi	2⁶⁰	2⁶¹		-	-	0.116	-	-
2012-09-14T10:25:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.233	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.743	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.766 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	299 / 100	2.990	4.954%
25	50000	299 / 280	1.068	34.309%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	20.766 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.199	0.001%
25	50000	1.351	25.899%
30	250000	0.113	89.347%
35	1000000	0.008	99.238%

ECM Summary

B1	B2	factor	curves	GHz-days
		8399774438446404972583	1	0.00000e+0
50000	5000000		249	9.63
250000	35000000		50	11.13

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-17T22:01:00	Steve Scott	Celeron	50000	5000000						1	0.039
2008-09-08T16:35:00	Sturle Sunde	v21	50000	5000000						3	0.116
2009-03-17T22:08:00	Sturle Sunde	v23	50000	5000000						3	0.116
2009-07-22T18:42:00	Geoff Wing	GW1	50000	5000000						3	0.116
2009-11-05T16:17:00	SubPrime	c2d0	50000	5000000						3	0.116
2010-05-10T11:46:00	greensinoz	giopa01	50000	5000000						3	0.116
2011-02-12T20:28:00	Bruce	dell-gx260	50000	5000000						3	0.116
2011-11-13T22:23:00	Oscar Östlin		50000	5000000						1	0.039
2012-03-12T13:12:00	unconnected	can-01	50000	5000000						3	0.116
2012-10-11T10:32:00	OS1	Tina	50000	5000000						3	0.116
2013-08-10T15:08:00	OS1	Tina	50000	5000000						3	0.116
2014-02-02T14:19:00	jim f in mn	asus	50000	5000000						3	0.116
2014-03-09T18:09:00	Bruce	snowflake			8399774438446404972583	72.831		1		1	-
2018-05-25T15:43:02	TJAOI	Manual testing	50000	5000000						217	8.394
2021-05-28T18:39:45	TJAOI	Manual testing	250000	35000000						50	11.13

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, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (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