M1332343 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	22.3020	68.6567%	500000	15000000	0.0714	4.8779%	22.3734	70.1856%	1.5289%
PrimeNet	2⁵⁶	0.0072	62.5000%	6000	100000	0.0006	2.6062%	0.0078	63.4773%	0.9773%
GPU72	2⁶⁰	0.1153	65.0000%	5500	40000	0.0004	0.9787%	0.1157	65.3425%	0.3425%
Difference	+7	+22.1867	+3.6567%	+494500	+14960000	+0.0710	+3.8992%	+22.2577	+4.8431%	+4.8431%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.3020

68.6567%

500000

15000000

0.0714

4.8779%

22.3734

70.1856%

1.5289%

PrimeNet

2⁵⁶

0.0072

62.5000%

6000

100000

0.0006

2.6062%

0.0078

63.4773%

0.9773%

GPU72

2⁶⁰

0.1153

65.0000%

5500

40000

0.0004

0.9787%

0.1157

65.3425%

0.3425%

Difference

+22.1867

+3.6567%

+494500

+14960000

+0.0710

+3.8992%

+22.2577

+4.8431%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1332343	127904929	9	26.930	48 2⁴ × 3	-	16	16	6.780e-12	8.858e-7	1.803e-6
1332343	2381635495273733177	19	61.047	893777163716 2² × 1657 × 134848697	2016-03-29	1657	134848697	0.3561	0.4068	0.7597
1332343	1494663313325683647127	22	70.340	560915362382541 3 × 521 × 6299 × 56972693	2018-05-27	6299	56972693	350.32	0.1722	0.3210
1332343	2057682295740741436092401	25	80.767	772204415732563400 2³ × 5² × 20341 × 189814762237	2021-06-04	20341	189814762237	234,706	572.53	1,069.3
1332343	68728531205433299601597736558159	32	105.761	25792356474809151848134353 3⁴ × 7 × 101 × 7741 × 39857 × 140813 × 10366739	2015-01-12	140813	10366739	1.123e+11	0.0386	0.0584

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1332343

127904929

26.930

48
2⁴ × 3

6.780e-12

8.858e-7

1.803e-6

1332343

2381635495273733177

61.047

893777163716
2² × 1657 × 134848697

2016-03-29

1657

134848697

0.3561

0.4068

0.7597

1332343

1494663313325683647127

70.340

560915362382541
3 × 521 × 6299 × 56972693

2018-05-27

6299

56972693

350.32

0.1722

0.3210

1332343

2057682295740741436092401

80.767

772204415732563400
2³ × 5² × 20341 × 189814762237

2021-06-04

20341

189814762237

234,706

572.53

1,069.3

1332343

68728531205433299601597736558159

105.761

25792356474809151848134353
3⁴ × 7 × 101 × 7741 × 39857 × 140813 × 10366739

2015-01-12

140813

10366739

1.123e+11

0.0386

0.0584

exponent	prime factors	composite factor	digits	bits*
1332343	127904929 2381635495273733177	304622918926866677569129433	27	87.977
1332343	127904929 1494663313325683647127	191174804969826320762239988983	30	97.271
1332343	127904929 2057682295740741436092401	263187707941276535790756587344529	33	107.698
1332343	2381635495273733177 1494663313325683647127	3559743200499893606440703793290020632479	40	131.387
1332343	127904929 68728531205433299601597736558159	8790717904105230599778086781032031265711	40	132.691
1332343	2381635495273733177 2057682295740741436092401	4900649193532493033884703043010610391287977	43	141.814
1332343	1494663313325683647127 2057682295740741436092401	3075542237923455858651748741734177749050181927	46	151.108
1332343	127904929 2381635495273733177 1494663313325683647127	455308701318171656239352161390790765405761588991	48	158.317
1332343	2381635495273733177 68728531205433299601597736558159	16368630945688836238354142486010878895777890834114 3	51	166.807
1332343	127904929 2381635495273733177 2057682295740741436092401	62681718715268078069201753690235606834435091673863 3	51	168.744
1332343	1494663313325683647127 68728531205433299601597736558159	10272601417152057788771299970990117503937636326875 9193	54	176.101
1332343	127904929 1494663313325683647127 2057682295740741436092401	39337701157810072903548595853734934186564333681001 8183	54	178.038
1332343	2057682295740741436092401 68728531205433299601597736558159	14142148187368517929927227458881698968383262763203 4449759	57	186.528
1332343	127904929 2381635495273733177 68728531205433299601597736558159	20936285789355334551593136715291049583920695269071 403193847	59	193.738
1332343	127904929 1494663313325683647127 68728531205433299601597736558159	13139163549061333336766901200271930390428005948168 852498762297	62	203.031
1332343	2381635495273733177 1494663313325683647127 2057682295740741436092401	73248205610521155138151851021437117014577647782809 13896305692079	64	212.154
1332343	127904929 2057682295740741436092401 68728531205433299601597736558159	18088504598128489826625690032951141259504344685158 804421978962111	65	213.458
1332343	2381635495273733177 1494663313325683647127 68728531205433299601597736558159	24465592163888594464000675518810497009077809642445 2710672619093747846161	72	237.148
1332343	127904929 2381635495273733177 1494663313325683647127 2057682295740741436092401	93688065379911100009432976961154919297142460046472 1033962092907660357391	72	239.085
1332343	2381635495273733177 2057682295740741436092401 68728531205433299601597736558159	33681442102457948100391783365751750620127785686530 2775306803372610977954343	75	247.575
1332343	1494663313325683647127 2057682295740741436092401 68728531205433299601597736558159	21137750067275040160917602714796083115660301924256 3700401559688903417766192393	78	256.868
1332343	127904929 2381635495273733177 1494663313325683647127 68728531205433299601597736558159	31292698286651270388277994581854947844008095977924 777822438887429862607125627569	80	264.078
1332343	127904929 2381635495273733177 2057682295740741436092401 68728531205433299601597736558159	43080224607324945772662959235798586946931503991628 714039119638590767679870806656647	83	274.505
1332343	127904929 1494663313325683647127 2057682295740741436092401 68728531205433299601597736558159	27036224215745592352543145500862002603866297057405 743877838763498453737242176627005097	86	283.799
1332343	2381635495273733177 1494663313325683647127 2057682295740741436092401 68728531205433299601597736558159	50342415850446977055339034871917279861571722163631 5252659959403789332488176078359087621929122561	96	317.915
1332343	127904929 2381635495273733177 1494663313325683647127 2057682295740741436092401 68728531205433299601597736558159	64390431250398952185277683262211037745674609517470 16621308916868455690285755464201753878762326419700 3169	104	344.845

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-01-12T12:27:00	alpertron	Manual testing	500000	15000000	12		68728531205433299601597736558159	32	105.761	0.071	0.102	0.143	4.878%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-01-12T12:27:00

alpertron

Manual testing

500000

15000000

68728531205433299601597736558159

105.761

0.071

0.102

0.143

4.878%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2016-03-29T11:14:34	TJAOI	Manual testing	2⁶¹	2⁶²*	2381635495273733177	61.047	19	0.126	0.103	0.255

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2016-03-29T11:14:34

TJAOI

Manual testing

2⁶¹

2⁶²*

2381635495273733177

61.047

0.126

0.103

0.255

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.285 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	304 / 100	3.040	4.711%
25	50000	304 / 280	1.086	33.700%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.285 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.360	0.000%
25	50000	1.366	25.525%
30	250000	0.114	89.267%
35	1000000	0.008	99.234%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.71
50000	5000000	1494663313325683647127	3	0.140
250000	35000000		39	10.48
250000	35000000	2057682295740741436092401	11	2.955

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