M4397 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	56.0550%	1.0484	56.0550%	-11.4450%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4514%	0.0000	68.2967%	0.7967%
GPU72	2⁴⁴	0.0005	70.4545%	500	10000	0.0000	0.9783%	0.0005	70.7436%	0.2890%
Difference	-44	-0.0005	-70.4545%	+999999500	+200999990000	+1.0484	+55.0767%	+1.0479	-14.6886%	-14.6886%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4397	149118978601	12	37.118	16956900 2² × 3² × 5² × 83 × 227	-	83	227	5.516e-6	8.006e-9	1.489e-8
4397	1432803526457417	16	50.348	162929670964 2² × 17 × 29 × 2957 × 27941	-	2957	27941	0.0527	3.806e-7	5.304e-7
4397	28904185208729874671204375707341034358742812377119 1294135823	60	197.525	32868075061098333717539658525518574435686618577574 629763 107 × 317 × 969016629649999519960484050989668753079000518222077	2020-10-01	317	969016629649999519960484050989668753079000518222077	3.578e+13	4.653e+39	8.690e+39

exponent	prime factors	composite factor	digits	bits*
4397	149118978601 1432803526457417	213658198401240902960733617	27	87.465
4397	149118978601 28904185208729874671204375707341034358742812377119 1294135823	43101625756199308994847372120005519411505751961261 854010517286724523623	71	234.643
4397	1432803526457417 28904185208729874671204375707341034358742812377119 1294135823	41414018496446476096061313262585270036618664414365 7913549357325501623749191	75	247.873
4397	149118978601 1432803526457417 28904185208729874671204375707341034358742812377119 1294135823	61756161379530202635104249927874103765283451052030 126380430922978779223446366120061791	86	284.990

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-07-06T07:06:21	ViliamF	3	1000000000	201000000000		-		-	-	1.048	-	-	48.045%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.532 GHz-days
Estimated T-Level:	33.484

Digits	B1	Curves	Complete	FacMiss
20	11000	1205 / 100	12.050	0.001%
25	50000	1205 / 280	4.304	1.342%
30	250000	1205 / 640	1.883	15.194%
35	1000000	1101 / 1580	0.697	49.805%
40	3000000	1101 / 4700	0.234	79.114%
45	11000000	315 / 9700	0.032	96.805%
50	44000000	201 / 17100	0.012	98.831%

New Calculation Method

Total ECM effort:	20.532 GHz-days
Estimated T-Level:	33.484

Digits	B1	Complete	FacMiss
20	11000	263.267	0.000%
25	50000	74.391	0.000%
30	250000	17.158	0.000%
35	1000000	3.412	3.296%
40	3000000	0.597	55.048%
45	11000000	0.096	90.884%
50	44000000	0.014	98.606%
55	110000000	0.002	99.807%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		786	2.990
11000000	11000000		104	0.984
11000000	1100000000		114	1.590
44000000	4400000000		200	11.16
110000000	900514153782	28904185208729874671204375707341034358742812377119 1294135823	1	3.809

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-12T04:23:00	unconnected	E5430-next	44000000	4400000000						200	11.16
2009-10-12T11:22:00	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2009-10-13T13:50:00	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2010-06-28T23:23:00	James Hintz	NEW_OMFG	3000000	300000000						784	2.983
2011-01-02T09:14:00	James Hintz	OMFG	11000000	1100000000						3	0.042
2011-01-30T00:00:00	James Hintz	OMFG	11000000	1100000000						11	0.153
2016-10-04T10:45:38	kkmrkkblmbrbk	kel1	11000000	11000000						104	0.984
2020-03-25T01:11:09	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.395
2020-10-01T02:17:25	Ryan Propper	Manual testing	110000000	900514153782	28904185208729874671204375707341034358742812377119 1294135823	197.525	1	2	1673610197772850481	1	3.809

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:34:35

Oliver Kruse

Oliver-PC

149118978601

1432803526457417

AE21FC6EF69470__

2017-09-21T19:21:12

Oliver Kruse

Manual testing

149118978601

1432803526457417

AE21FC6EF69470__

2017-10-12T13:52:42

kkmrkkblmbrbk

Manual testing

149118978601

1432803526457417

AE21FC6EF69470__

2020-04-17T12:32:25

Oliver Kruse

IOS-1

149118978601

1432803526457417

42CB08130A252F__

2020-10-01T02:22:21

M Miller

cruncher

149118978601

1432803526457417

28904185208729874671204375707341034358742812377119
1294135823

42CB08130A252F9A

2020-10-01T15:22:06

mnd9

149118978601

1432803526457417

28904185208729874671204375707341034358742812377119
1294135823

42CB08130A252F9A

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)

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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