M1249 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	23,790.1662	83.5821%	1000000000000	2232843418649129478	2,876,234.7953	43.3970%	2,900,024.9614	90.7070%	7.1249%
PrimeNet	2⁴⁰	0.0001	72.5000%	500	10000	0.0000	1.7007%	0.0001	72.9677%	0.4677%
GPU72	2⁴⁴	0.0019	75.0000%	500	10000	0.0000	0.6519%	0.0019	75.1630%	0.1630%
Difference	+23	+23,790.1643	+8.5821%	+999999999500	+2232843418649119478	+2,876,234.7953	+42.7452%	+2,900,024.9596	+15.5440%	+15.5440%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23,790.1662

83.5821%

1000000000000

2232843418649129478

2,876,234.7953

43.3970%

2,900,024.9614

90.7070%

7.1249%

PrimeNet

2⁴⁰

0.0001

72.5000%

500

10000

0.0000

1.7007%

0.0001

72.9677%

0.4677%

GPU72

2⁴⁴

0.0019

75.0000%

500

10000

0.0000

0.6519%

0.0019

75.1630%

0.1630%

Difference

+23

+23,790.1643

+8.5821%

+999999999500

+2232843418649119478

+2,876,234.7953

+42.7452%

+2,900,024.9596

+15.5440%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1249	97423	5	16.572	39 3 × 13	-	3	13	7.049e-12	8.381e-11	1.444e-10
1249	52358081	8	25.642	20960 2⁵ × 5 × 131	-	32	131	5.500e-9	8.841e-10	1.540e-9
1249	2379005273	10	31.148	952364 2² × 7² × 43 × 113	-	49	113	2.610e-7	1.241e-9	2.358e-9
1249	9345276045907272726364012481	28	92.916	3741103301003712060193760 2⁵ × 5 × 450421 × 121523473 × 427170167	-	121523473	427170167	1.349e+12	0.0033	0.0058

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1249

97423

16.572

39
3 × 13

7.049e-12

8.381e-11

1.444e-10

1249

52358081

25.642

20960
2⁵ × 5 × 131

131

5.500e-9

8.841e-10

1.540e-9

1249

2379005273

31.148

952364
2² × 7² × 43 × 113

113

2.610e-7

1.241e-9

2.358e-9

1249

9345276045907272726364012481

92.916

3741103301003712060193760
2⁵ × 5 × 450421 × 121523473 × 427170167

121523473

427170167

1.349e+12

0.0033

0.0058

exponent	prime factors	composite factor	digits	bits*
1249	97423 52358081	5100881325263	13	42.214
1249	97423 2379005273	231769830711479	15	47.720
1249	52358081 2379005273	124560150783161113	18	56.790
1249	97423 52358081 2379005273	12135023569747905111799	23	73.362
1249	97423 9345276045907272726364012481	910444828220424230820561187936463	33	109.488
1249	52358081 9345276045907272726364012481	489300720178972703896057800965208961	36	118.558
1249	2379005273 9345276045907272726364012481	22232460990853991885069071809736812313	38	124.064
1249	97423 52358081 9345276045907272726364012481	47669144061996057731665639143433552607503	41	135.130
1249	97423 2379005273 9345276045907272726364012481	2165953047111968451419084182919989465969399	43	140.636
1249	52358081 2379005273 9345276045907272726364012481	1164048993388473566291789152409016607765851353	46	149.706
1249	97423 52358081 2379005273 9345276045907272726364012481	11340514508288526024884497459514362497837253636331 9	51	166.278

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-09-07T20:58:12	kkmrkkblmbrbk	Manual testing	1000000000	100000000000	12	-	skipped known factors(?)	-	-	0.151	-	-	14.632%
2021-03-27T16:37:19	nordi	Manual testing	1000000000000	2232843418649129478		-	skipped known factors(?)	-	-	2,876,235	-	-	43.397%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-09-07T20:58:12

kkmrkkblmbrbk

Manual testing

1000000000

100000000000

skipped known factors(?)

0.151

-

-

14.632%

2021-03-27T16:37:19

nordi

Manual testing

1000000000000

2232843418649129478

skipped known factors(?)

2,876,235

-

-

43.397%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-07-19T06:17:57	ViliamF	3	1000000000	221000000000	2	7			-	-	0.314

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-07-19T06:17:57

ViliamF

1000000000

221000000000

0.314

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2005-01-20T00:00:00	ANONYMOUS	v4_computers	?	?	97423 52358081 2379005273	73.362	23	1,110,938	6.47901e-8	3,534,277
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	97423 52358081 2379005273	73.362	23	1,110,938	6.47901e-8	3,534,277

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2005-01-20T00:00:00

ANONYMOUS

v4_computers

97423
52358081
2379005273

73.362

1,110,938

6.47901e-8

3,534,277

2009-10-25T00:00:00

Carsten Kossendey

v4_computers

97423
52358081
2379005273

73.362

1,110,938

6.47901e-8

3,534,277

ECM factoring results:

Old Calculation Method

Total ECM effort:	24,496.977 GHz-days
Estimated T-Level:	54.941

Digits	B1	Curves	Complete	FacMiss
20	11000	47620 / 100	476.200	0.000%
25	50000	47620 / 280	170.071	0.000%
30	250000	47620 / 640	74.406	0.000%
35	1000000	46980 / 1580	29.734	0.000%
40	3000000	46980 / 4700	9.996	0.005%
45	11000000	46969 / 9700	4.842	0.789%
50	44000000	46969 / 17100	2.747	6.413%
55	110000000	45950 / 46500	0.988	37.225%
60	260000000	36991 / 112000	0.330	71.872%
65	800000000	25687 / 360000	0.071	93.113%

New Calculation Method

Total ECM effort:	24,496.977 GHz-days
Estimated T-Level:	54.941

Digits	B1	Complete	FacMiss
20	11000	21,877.200	0.000%
25	50000	10,355.724	0.000%
30	250000	3,659.975	0.000%
35	1000000	1,181.239	0.000%
40	3000000	332.652	0.000%
45	11000000	84.880	0.000%
50	44000000	19.553	0.000%
55	110000000	4.141	1.591%
60	260000000	0.814	44.294%

ECM Summary

B1	B2	curves	GHz-days
250000	25000000	640	0.054
44000000	4400000000	1,019	15.25
110000000	11000000000	8,958	335.2
260000000	26000000000	9,372	829.0
260000000	2600000000000	1,598	4,693
260000000	5200000000000	334	1,942
850000000	85000000000	18,160	5,252
2900000000	290000000000	5,016	4,949
5000000000	500000000000	15	25.52
7600000000	760000000000	2,496	6,454
various		12	2.2705

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-22T16:35:00	Jayson King	atlas	44000000	4400000000						1000	14.97
2009-10-13T09:51:00	Carsten Kossendey	durandal	44000000	4400000000						1	0.015
2010-12-29T19:04:00	ANONYMOUS	13_052010	44000000	4400000000						3	0.045
2010-12-31T06:13:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-01-02T09:09:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-01-05T02:25:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-01-07T02:14:00	James Hintz	13_052010	44000000	4400000000						3	0.045
2011-01-11T15:37:00	James Hintz	17_051310	44000000	4400000000						3	0.045
2011-01-12T15:00:00	James Hintz	NEW_OMFG	3000000	300000000						11	0.011
2011-04-18T06:17:00	Matthias Wurtinger	i5-750	110000000	11000000000						2000	74.85
2011-04-19T07:42:00	Matthias Wurtinger	i5-750	110000000	11000000000						2000	74.85
2011-04-20T21:43:00	Matthias Wurtinger	i5-750	110000000	11000000000						770	28.82
2013-05-03T20:20:00	Never Odd Or Even	Note	200000000	2000000000000						1	2.259
2014-06-03T20:56:00	Matthias Wurtinger	i5-4670K	110000000	11000000000						746	27.92
2014-06-04T16:24:00	Matthias Wurtinger	i5-750	110000000	11000000000						550	20.58
2014-06-18T13:57:00	Matthias Wurtinger	i5-750	110000000	11000000000						1600	59.88
2014-06-30T16:16:00	Matthias Wurtinger	i5-4670K	110000000	11000000000						1292	48.35
2015-04-28T13:51:00	Matthias Wurtinger	i5-750	260000000	2600000000000						1598	4,693
2015-05-01T21:04:00	Matthias Wurtinger	i5-4670K	260000000	5200000000000						334	1,942
2016-02-16T12:17:15	BloodIce	Mjolnir4	5000000000	500000000000						15	25.52
2019-11-16T04:38:03	Ryan Propper	Manual testing	260000000	26000000000						4036	357.0
2019-11-16T04:38:03	Ryan Propper	Manual testing	850000000	85000000000						4080	1,180
2019-11-16T04:38:03	Ryan Propper	Manual testing	2900000000	290000000000						1116	1,101
2019-11-16T04:38:03	Ryan Propper	Manual testing	7600000000	760000000000						648	1,676
2019-11-19T03:23:55	Ryan Propper	Manual testing	260000000	26000000000						5336	472.0
2019-11-19T03:23:55	Ryan Propper	Manual testing	850000000	85000000000						14080	4,072
2019-11-19T03:23:55	Ryan Propper	Manual testing	2900000000	290000000000						3900	3,848
2019-11-19T03:23:55	Ryan Propper	Manual testing	7600000000	760000000000						1848	4,778
2021-10-02T00:37:41	_p95holder_	TFL3_PRPt20pE_h	250000	25000000						640	0.054

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