M31327 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	unknown	200000000	5000000000	0.3686	48.9045%	0.3686	48.9045%	48.9045%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1490%	0.0000	64.0559%	1.5559%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7811%	0.0001	66.5163%	0.6072%
Difference	-44	-0.0001	-65.9091%	+199999500	+4999990000	+0.3686	+47.1234%	+0.3685	-17.6118%	-17.6118%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31327	64972199	8	25.953	1037 17 × 61	-	17	61	1.747e-10	1.549e-8	2.763e-8
31327	132717395548777697201387407	27	86.778	2118258938755349972889 3 × 309347741 × 2282500304143	2015-04-24	309347741	2282500304143	917,024,873	99.56	185.51
31327	323925290824739231872617894688159	33	107.997	5170065611529020204178789777 3³ × 19 × 10078100607269045232317329	2017-06-05	27	10078100607269045232317329	5.161e+12	4.386e+14	8.191e+14

exponent	prime factors	composite factor	digits	bits*
31327	64972199 132717395548777697201387407	8622941034356898749330285683697993	34	112.732
31327	64972199 323925290824739231872617894688159	21046138456597831496334872504640109491641	41	133.951
31327	132717395548777697201387407 323925290824739231872617894688159	42990520950639767572524919486916170791759701302870 414613713	59	194.776
31327	64972199 132717395548777697201387407 323925290824739231872617894688159	27931886823186361560358360013628953450001988732306 55849494669164887	67	220.729

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-09T01:59:40	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 64972199	-	-	0.369	-	-	41.255%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.209 GHz-days
Estimated T-Level:	34.782

Digits	B1	Curves	Complete	FacMiss
20	11000	2377 / 100	23.770	0.000%
25	50000	2377 / 280	8.489	0.020%
30	250000	2096 / 640	3.275	3.772%
35	1000000	1511 / 1580	0.956	38.418%

New Calculation Method

Total ECM effort:	19.209 GHz-days
Estimated T-Level:	34.782

Digits	B1	Complete	FacMiss
20	11000	273.672	0.000%
25	50000	51.039	0.000%
30	250000	7.527	0.054%
35	1000000	0.888	41.142%
40	3000000	0.086	91.741%
45	11000000	0.007	99.282%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	0.161
250000	25000000		523	1.503
250000	25000000	132717395548777697201387407	62	0.178
1000000	100000000		1,145	13.16
1000000	100000000	323925290824739231872617894688159	366	4.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T14:35:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-13T20:35:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13T20:55:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T02:14:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T14:57:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T21:18:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T02:18:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T07:34:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T12:45:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-23T22:13:00	James Hintz	home2	50000	5000000						163	0.094
2011-01-20T19:56:00	James Hintz	NEW_OMFG	250000	25000000						4	0.011
2011-03-17T02:24:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-06-20T11:34:00	James Hintz	08_04_2014	250000	25000000	132717395548777697201387407	86.778	62	2		62	0.178
2015-06-20T16:51:00	James Hintz	08_04_2014	250000	25000000						508	1.460
2015-06-20T17:18:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-06-05T11:38:37	nordi	nordiputer	1000000	100000000	323925290824739231872617894688159	107.997	366	2		366	4.207
2017-06-09T03:01:41	nordi	nordiputer	1000000	100000000						1134	13.03

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:41:35

Oliver Kruse

PRP

64972199

132717395548777697201387407

323925290824739231872617894688159

9DD1DFCBC248B369

2017-09-21T20:27:24

Oliver Kruse

Manual testing

64972199

132717395548777697201387407

323925290824739231872617894688159

9DD1DFCBC248B369

2017-10-02T10:35:57

kkmrkkblmbrbk

Manual testing

64972199

132717395548777697201387407

323925290824739231872617894688159

9DD1DFCBC248B3__

2017-12-07T03:12:54

ATH

xps

64972199

132717395548777697201387407

323925290824739231872617894688159

9DD1DFCBC248B3__

2020-04-17T13:47:34

Oliver Kruse

Manual testing

64972199

132717395548777697201387407

323925290824739231872617894688159

CA70BF0D1132EC__

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 = 200000000, B2 = 5000000000 (P-1 stage 2)

B1 = 200000000 (P-1 stage 1)

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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