M1882259 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	15.7863	68.6567%	500000	15000000	0.1015	5.0858%	15.8878	70.2508%	1.5941%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0328%	0.0116	64.2752%	1.1173%
GPU72	2⁶¹	0.1632	65.5738%	10000	150000	0.0014	1.6918%	0.1646	66.1562%	0.5824%
Difference	+6	+15.6231	+3.0829%	+490000	+14850000	+0.1001	+3.3940%	+15.7232	+4.0946%	+4.0946%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.7863

68.6567%

500000

15000000

0.1015

5.0858%

15.8878

70.2508%

1.5941%

PrimeNet

2⁵⁷

0.0102

63.1579%

9000

160000

0.0014

3.0328%

0.0116

64.2752%

1.1173%

GPU72

2⁶¹

0.1632

65.5738%

10000

150000

0.0014

1.6918%

0.1646

66.1562%

0.5824%

Difference

+15.6231

+3.0829%

+490000

+14850000

+0.1001

+3.3940%

+15.7232

+4.0946%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1882259	2789507839	10	31.377	741 3 × 13 × 19	-	13	19	1.764e-10	1.048e-6	2.081e-6
1882259	441323720836459317121	21	68.580	117232463979840 2⁶ × 3 × 5 × 11 × 373 × 29762893	2020-10-18	373	29762893	45.278	0.1276	0.2382
1882259	472793317946296812359	21	68.680	125591992904881 23 × 5460521430647	2021-10-28	23	5460521430647	53.122	23,402	43,709
1882259	1235269075829000901881	22	70.065	328134724240660 2² × 5 × 43 × 89 × 1583 × 2708213	2015-08-27	1583	2708213	218.79	0.0117	0.0217

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1882259

2789507839

31.377

741
3 × 13 × 19

1.764e-10

1.048e-6

2.081e-6

1882259

441323720836459317121

68.580

117232463979840
2⁶ × 3 × 5 × 11 × 373 × 29762893

2020-10-18

373

29762893

45.278

0.1276

0.2382

1882259

472793317946296812359

68.680

125591992904881
23 × 5460521430647

2021-10-28

5460521430647

53.122

23,402

43,709

1882259

1235269075829000901881

70.065

328134724240660
2² × 5 × 43 × 89 × 1583 × 2708213

2015-08-27

1583

2708213

218.79

0.0117

0.0217

exponent	prime factors	composite factor	digits	bits*
1882259	2789507839 441323720836459317121	1231075978809950902113616411519	31	99.958
1882259	2789507839 472793317946296812359	1318860666638014339096142582201	31	100.057
1882259	2789507839 1235269075829000901881	3445792770299283439335119345159	31	101.443
1882259	441323720836459317121 472793317946296812359	208654906262674845323147121296588213098439	42	137.260
1882259	441323720836459317121 1235269075829000901881	545153544779069089530092778675074384404601	42	138.646
1882259	472793317946296812359 1235269075829000901881	584026964917649050058940938094726427147279	42	138.745
1882259	2789507839 441323720836459317121 472793317946296812359	58204449666554167413703138300711666439309806916332 1	51	168.638
1882259	2789507839 441323720836459317121 1235269075829000901881	15207100866198507483667866325114120292047338371672 39	52	170.023
1882259	2789507839 472793317946296812359 1235269075829000901881	16291477968251600145903191588532530930877971780200 81	52	170.122
1882259	441323720836459317121 472793317946296812359 1235269075829000901881	25774495322628116868174498247329046109013215822080 5148433263759	63	207.325
1882259	2789507839 441323720836459317121 472793317946296812359 1235269075829000901881	71898156748739966085580892480816134933484814090292 4254446147824085106801	72	238.703

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-08-27T15:07:00	alpertron	Manual testing	500000	15000000	12		1235269075829000901881	22	70.065	0.101	0.204	0.203	5.086%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-08-27T15:07:00

alpertron

Manual testing

500000

15000000

1235269075829000901881

70.065

0.101

0.204

0.203

5.086%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.278 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	19.278 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.558	0.019%
25	50000	0.775	46.059%
30	250000	0.048	95.316%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	1.663
50000	5000000	441323720836459317121	4	0.277
50000	6438386		14	1.082
50000	6600000		126	9.85
50000	6600000	472793317946296812359	82	6.409

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-03-08T05:19:07	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-20T17:45:09	Ismo Laitela	6600K	50000	5000000						3	0.208
2020-07-17T03:38:56	nordi	sweet16	50000	5000000						3	0.208
2020-08-15T21:34:17	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.208
2020-10-18T13:34:32	nordi	sweet16	50000	5000000	441323720836459317121	68.580	4	2	362559465412725	4	0.277
2020-11-10T02:24:17	nordi	sweet16	50000	5000000						7	0.485
2021-02-11T16:12:15	seatsea	dt	50000	6438386						7	0.541
2021-06-01T09:04:15	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-07-14T09:05:41	seatsea	Manual testing	50000	6438386						7	0.541
2021-10-28T13:39:18	TJAOI	Manual testing	50000	6600000	472793317946296812359	68.680	82	2		82	6.409
2021-10-28T13:39:18	TJAOI	Manual testing	50000	6600000						126	9.85

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T14:09:32

Oliver Kruse

GTX-0

2789507839

1235269075829000901881

134B5AA5A82C9F__

2017-11-08T07:31:37

kkmrkkblmbrbk

c4.xlarge

2789507839

1235269075829000901881

134B5AA5A82C9F__

2020-10-21T18:46:11

arnaud

SRV-130

2789507839

441323720836459317121

1235269075829000901881

691E19E76D68E846

2021-10-29T13:44:00

JackBlock

Win10

2789507839

441323720836459317121

472793317946296812359

1235269075829000901881

691E19E76D68E846

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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