M4273 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	2⁶⁷	6,953.8773	80.5970%	1000000000	201000000000	0.8572	16.8111%	6,954.7345	83.8589%	16.3589%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4317%	0.0000	68.2903%	0.7903%
GPU72	2⁴⁴	0.0005	70.4545%	500	10000	0.0000	0.9695%	0.0005	70.7410%	0.2864%
Difference	+23	+6,953.8767	+10.1425%	+999999500	+200999990000	+0.8572	+15.8416%	+6,954.7339	+13.1179%	+13.1179%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4273	25639	5	14.646	3 3	-	1	3	5.111e-13	7.991e-11	1.466e-10
4273	719086079	9	29.422	84143 84143	-	1	84143	2.030e-8	3.304e-7	6.170e-7
4273	132767035316260947713	21	66.847	15535576330009472 2⁷ × 11 × 59 × 187013389951	-	128	187013389951	4,888.6	0.7342	1.3713
4273	58191431507503762014994956623	29	95.555	6809200972092647088110807 43 × 2897 × 54661205032412416117	-	2897	54661205032412416117	2.458e+12	214,592,299	400,798,655
4273	16937472485366180815044482979818421310092932459932 943	53	173.500	1981918147129204401479579098972434040497651820727 23 × 107830127681 × 5278569365895061 × 151391511755474276189	2020-10-01	5278569365895061	151391511755474276189	3.176e+13	594,701,683	1.110e+9

exponent	prime factors	composite factor	digits	bits*
4273	25639 719086079	18436647979481	14	44.068
4273	25639 132767035316260947713	3404014018473614438413607	25	81.494
4273	719086079 132767035316260947713	95470926846024609831765187327	29	96.269
4273	25639 58191431507503762014994956623	1491970112420888954302455692857097	34	110.201
4273	25639 719086079 132767035316260947713	2447779093405224971476627637876953	34	110.915
4273	719086079 58191431507503762014994956623	41844648314127939305111862562808151217	38	124.976
4273	25639 719086079 58191431507503762014994956623	1072854938125926235843763044247838189052663	43	139.622
4273	132767035316260947713 58191431507503762014994956623	7725903842060532011415773976564438303505306053199	49	162.402
4273	25639 132767035316260947713 58191431507503762014994956623	19808444860658998024068902898513563366357254189796 9161	54	177.048
4273	25639 16937472485366180815044482979818421310092932459932 943	43425985705230350991692549911956450396947269534022 0725577	57	188.147
4273	719086079 132767035316260947713 58191431507503762014994956623	55555899005183432447429521475579598305050424854898 34316721	58	191.824
4273	719086079 16937472485366180815044482979818421310092932459932 943	12179500677672351841495361476539864711844769928225 004584800497	62	202.922
4273	25639 719086079 132767035316260947713 58191431507503762014994956623	14243976945938980245196455011123853209431878428547 3862046409719	63	206.470
4273	25639 719086079 16937472485366180815044482979818421310092932459932 943	31227021787484142886409957289700559134698805618976 0892549699942583	66	217.568
4273	132767035316260947713 16937472485366180815044482979818421310092932459932 943	22487380076328098161721092667437435911713263933460 59012815697953609209359	73	240.348
4273	25639 132767035316260947713 16937472485366180815044482979818421310092932459932 943	57655393777697610876836709490042841934041637398999 607029581679832586518755401	77	254.994
4273	58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	98561577004241562598098816967940124939078818270081 8922200498194567129165773731489	81	269.055
4273	719086079 132767035316260947713 16937472485366180815044482979818421310092932459932 943	16170361966069492824639128417823236767567681134204 29265628250991109170256253413361	82	269.770
4273	25639 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	25270202728117494234526555682410168633130418216266 296346298573210506624681272701646471	86	283.701
4273	25639 719086079 132767035316260947713 16937472485366180815044482979818421310092932459932 943	41459191044805572653092261350456996748366777659986 385941442727161048016200081265162679	86	284.416
4273	719086079 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	70874257948036631617499931148014733149212301301786 7508854162298577856014102773577623841631	90	298.477
4273	25639 719086079 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	18171450995297111980410807347039497432126541930765 105059511867173237650345581011756697675577209	95	313.123
4273	132767035316260947713 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	13085728374948512441365740573899846831995919383695 29549254578050918636222163475484459485186315306346 57	102	335.903
4273	25639 132767035316260947713 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	33550498980530491048417622257421817292554337707856 36811333812664750291410004934794605674069193813941 970823	106	350.549
4273	719086079 132767035316260947713 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	94097651080007676383444077942168505971205174136215 46566481119034345444690229064831325966369860580984 3883639903	110	365.324
4273	25639 719086079 132767035316260947713 58191431507503762014994956623 16937472485366180815044482979818421310092932459932 943	24125696760403168147951227143592583245957294596784 28324180094109215828564127829932103664517568554358 587332643473017	115	379.970

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-07-05T10:47:59	ViliamF	3	1000000000	201000000000		-		-	-	0.857	-	-	16.811%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	25639 719086079	44.068	14	0.000	4.98013e-7	0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.937 GHz-days
Estimated T-Level:	33.807

Digits	B1	Curves	Complete	FacMiss
20	11000	1304 / 100	13.040	0.000%
25	50000	1304 / 280	4.657	0.941%
30	250000	1304 / 640	2.038	13.015%
35	1000000	1203 / 1580	0.761	46.690%
40	3000000	1203 / 4700	0.256	77.415%
45	11000000	418 / 9700	0.043	95.782%
50	44000000	201 / 17100	0.012	98.831%

New Calculation Method

Total ECM effort:	17.937 GHz-days
Estimated T-Level:	33.807

Digits	B1	Complete	FacMiss
20	11000	288.517	0.000%
25	50000	82.863	0.000%
30	250000	19.156	0.000%
35	1000000	3.812	2.211%
40	3000000	0.664	51.491%
45	11000000	0.105	90.009%
50	44000000	0.015	98.484%
55	110000000	0.002	99.793%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		785	2.442
11000000	11000000		101	0.781
11000000	1100000000		217	2.475
44000000	4400000000		200	9.125
110000000	900514153782	16937472485366180815044482979818421310092932459932 943	1	3.114

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-01T04:44:00	unconnected	E5430-next	44000000	4400000000						200	9.125
2009-10-13T13:30:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2010-06-17T22:37:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T01:03:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T03:29:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T05:57:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T08:31:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T11:05:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T17:24:00	James Hintz	16_061510	3000000	300000000						100	0.311
2010-06-18T20:46:00	James Hintz	16_061510	3000000	300000000						84	0.261
2011-01-02T03:53:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-14T03:35:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-29T06:43:00	James Hintz	OMFG	11000000	1100000000						11	0.125
2016-10-02T23:29:16	kkmrkkblmbrbk	kel1	11000000	11000000						101	0.781
2020-03-18T17:21:20	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-08-12T18:40:37	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-10-01T03:41:55	Ryan Propper	Manual testing	110000000	900514153782	16937472485366180815044482979818421310092932459932 943	173.500	1	2	3652384067019655305	1	3.114

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:48

Oliver Kruse

Oliver-PC

0EA99051603194__

2017-09-21T19:21:11

Oliver Kruse

Manual testing

0EA99051603194__

2017-10-02T09:55:58

kkmrkkblmbrbk

Manual testing

25639

719086079

132767035316260947713

58191431507503762014994956623

0EA99051603194__

2017-12-07T02:44:27

ATH

Manual testing

25639

719086079

132767035316260947713

58191431507503762014994956623

0EA99051603194__

2020-04-17T12:32:21

Oliver Kruse

IOS-1

25639

719086079

132767035316260947713

58191431507503762014994956623

8AFA05C962E70F__

2020-10-01T03:44:26

M Miller

cruncher

25639

719086079

132767035316260947713

58191431507503762014994956623

16937472485366180815044482979818421310092932459932
943

8AFA05C962E70FEF

2020-10-01T05:09:24

Team_Inspector

Purple

25639

719086079

132767035316260947713

58191431507503762014994956623

16937472485366180815044482979818421310092932459932
943

8AFA05C962E70FEF

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