M4327 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	1000000000	201000000000	1.0484	56.0272%	1.0484	56.0272%	-11.4728%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4403%	0.0000	68.2931%	0.7931%
GPU72	2⁴⁴	0.0005	70.4545%	500	10000	0.0000	0.9734%	0.0005	70.7421%	0.2876%
Difference	-44	-0.0005	-70.4545%	+999999500	+200999990000	+1.0484	+55.0539%	+1.0479	-14.7149%	-14.7149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4327	946574521	9	29.818	109380 2² × 3 × 5 × 1823	-	5	1823	2.769e-8	9.170e-9	1.634e-8
4327	354536752771249	15	48.333	40967963112 2³ × 3 × 67 × 643 × 39623	-	643	39623	0.0129	2.438e-7	3.553e-7
4327	161510437409675503	18	57.164	18663096534513 3 × 6221032178171	-	3	6221032178171	6.7736	29.870	55.789
4327	621316165862254523582603721415095832031	39	128.869	71795258361711870069632969888501945 5 × 137 × 1733 × 461443 × 131065553611884047254963	2020-09-30	461443	131065553611884047254963	4.298e+13	6.293e+11	1.175e+12

exponent	prime factors	composite factor	digits	bits*
4327	946574521 354536752771249	335595456931340444746729	24	78.151
4327	946574521 161510437409675503	152881664927564070017659063	27	86.983
4327	354536752771249 161510437409675503	57261386017890409549361078013247	32	105.497
4327	946574521 354536752771249 161510437409675503	54202169041680711849680288276432910679687	41	135.315
4327	946574521 621316165862254523582603721415095832031	588122052090620127640286321531311779373840282151	48	158.687
4327	354536752771249 621316165862254523582603721415095832031	22027941588908646979338166615218045759467954867007 6719	54	177.202
4327	161510437409675503 621316165862254523582603721415095832031	10034904571811522268070368330630692784860666432750 3436593	57	186.033
4327	946574521 354536752771249 621316165862254523582603721415095832031	20851088258137181427225121960818212975324460593087 4057320676599	63	207.020
4327	946574521 161510437409675503 621316165862254523582603721415095832031	94987849883432017931795424968603176507276413803214 352618872846953	65	215.851
4327	354536752771249 161510437409675503 621316165862254523582603721415095832031	35577424812594179772024064331124714360849266292537 373934442863904914657	71	234.366
4327	946574521 354536752771249 161510437409675503 621316165862254523582603721415095832031	33676683850394850485091567894707561887382715394060 010606593139302662780995654297	80	264.184

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-07-05T18:34:56	ViliamF	3	1000000000	201000000000		-		-	-	1.048	-	-	48.016%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.529 GHz-days
Estimated T-Level:	33.481

Digits	B1	Curves	Complete	FacMiss
20	11000	1204 / 100	12.040	0.001%
25	50000	1204 / 280	4.300	1.346%
30	250000	1204 / 640	1.881	15.218%
35	1000000	1100 / 1580	0.696	49.836%
40	3000000	1100 / 4700	0.234	79.131%
45	11000000	315 / 9700	0.032	96.805%
50	44000000	201 / 17100	0.012	98.831%

New Calculation Method

Total ECM effort:	20.529 GHz-days
Estimated T-Level:	33.481

Digits	B1	Complete	FacMiss
20	11000	263.067	0.000%
25	50000	74.344	0.000%
30	250000	17.149	0.000%
35	1000000	3.411	3.301%
40	3000000	0.597	55.058%
45	11000000	0.096	90.886%
50	44000000	0.014	98.606%
55	110000000	0.002	99.807%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		785	2.986
11000000	11000000		104	0.984
11000000	1100000000		114	1.590
44000000	4400000000		200	11.16
110000000	900514153782	621316165862254523582603721415095832031	1	3.809

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-15T16:09:00	unconnected	E5430-next	44000000	4400000000						200	11.16
2009-10-13T13:34:00	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2010-06-22T12:56:00	James Hintz	NEW_OMFG	3000000	300000000						784	2.983
2011-01-02T05:49:00	James Hintz	OMFG	11000000	1100000000						3	0.042
2011-01-29T12:54:00	James Hintz	OMFG	11000000	1100000000						11	0.153
2016-10-03T11:48:28	kkmrkkblmbrbk	kel1	11000000	11000000						104	0.984
2020-03-23T22:13:44	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.395
2020-09-30T15:48:30	Ryan Propper	Manual testing	110000000	900514153782	621316165862254523582603721415095832031	128.869	1	2	16856555402872410790	1	3.809

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:50

Oliver Kruse

Oliver-PC

08ECBE5F22C5E8__

2017-09-21T19:21:11

Oliver Kruse

Manual testing

08ECBE5F22C5E8__

2017-10-02T09:55:58

kkmrkkblmbrbk

Manual testing

946574521

354536752771249

161510437409675503

08ECBE5F22C5E8__

2017-12-07T02:44:28

ATH

Manual testing

946574521

354536752771249

161510437409675503

08ECBE5F22C5E8__

2020-04-17T12:32:23

Oliver Kruse

IOS-1

946574521

354536752771249

161510437409675503

56BC5AF53E8E68__

2020-10-01T15:22:06

mnd9

946574521

354536752771249

161510437409675503

621316165862254523582603721415095832031

56BC5AF53E8E68EE

2020-10-03T00:39:41

fre_games

gpu

946574521

354536752771249

161510437409675503

621316165862254523582603721415095832031

56BC5AF53E8E68EE

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 = 1000000000, B2 = 201000000000 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

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