M5214289 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	5.6986	65.6716%	2500000	6555248700	82.3207	14.5699%	88.0193	70.6733%	5.0016%
PrimeNet	2⁶²	0.1178	62.9032%	22000	500000	0.0110	3.0042%	0.1288	64.0177%	1.1145%
GPU72	2⁶⁶	2.8323	65.1515%	30000	600000	0.0140	1.9881%	2.8463	65.8444%	0.6928%
Difference	+1	+2.8663	+0.5201%	+2470000	+6554648700	+82.3067	+12.5818%	+85.1730	+4.8289%	+4.8289%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.6986

65.6716%

2500000

6555248700

82.3207

14.5699%

88.0193

70.6733%

5.0016%

PrimeNet

2⁶²

0.1178

62.9032%

22000

500000

0.0110

3.0042%

0.1288

64.0177%

1.1145%

GPU72

2⁶⁶

2.8323

65.1515%

30000

600000

0.0140

1.9881%

2.8463

65.8444%

0.6928%

Difference

+2.8663

+0.5201%

+2470000

+6554648700

+82.3067

+12.5818%

+85.1730

+4.8289%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5214289	1866715463	10	30.798	179 179	-	1	179	2.850e-11	2.450e-6	4.182e-6
5214289	15976581497	11	33.895	1532 2² × 383	2008-09-08	4	383	2.922e-10	5.644e-6	8.892e-6
5214289	413802557920726033831	21	68.488	39679672331235 3 × 5 × 171673 × 15409013	2022-01-26	171673	15409013	20.253	0.2294	0.3590
5214289	468939591342953500433	21	68.668	44966781793544 2³ × 13 × 19 × 29 × 784705811	2022-01-26	29	784705811	14.667	9.790	18.284

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5214289

1866715463

30.798

179
179

179

2.850e-11

2.450e-6

4.182e-6

5214289

15976581497

33.895

1532
2² × 383

2008-09-08

383

2.922e-10

5.644e-6

8.892e-6

5214289

413802557920726033831

68.488

39679672331235
3 × 5 × 171673 × 15409013

2022-01-26

171673

15409013

20.253

0.2294

0.3590

5214289

468939591342953500433

68.668

44966781793544
2³ × 13 × 19 × 29 × 784705811

2022-01-26

784705811

14.667

9.790

18.284

exponent	prime factors	composite factor	digits	bits*
5214289	1866715463 15976581497	29823731726329588111	20	64.693
5214289	1866715463 413802557920726033831	772451633499572415538988828753	30	99.285
5214289	1866715463 468939591342953500433	875376786372792235348258295479	30	99.466
5214289	15976581497 413802557920726033831	6611150290287542344910550625007	31	102.383
5214289	15976581497 468939591342953500433	7492051598260572276349249288201	31	102.563
5214289	1866715463 15976581497 413802557920726033831	12341136475096694011511804203544881383241	41	133.181
5214289	1866715463 15976581497 468939591342953500433	13985528568066874171490252834726550152063	41	133.361
5214289	413802557920726033831 468939591342953500433	194048402408014112454803526544134231148823	42	137.155
5214289	1866715463 413802557920726033831 468939591342953500433	36223315334548637884160263162686632123312414835004 9	51	167.953
5214289	15976581497 413802557920726033831 468939591342953500433	31002301154342885135602912709553633112566065951280 31	52	171.051
5214289	1866715463 15976581497 413802557920726033831 468939591342953500433	57872474953394613286662808982762994759055894920332 75932443353	61	201.849

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-26T10:58:35	happy5214	Manual testing	2500000	6555248700			413802557920726033831 468939591342953500433	42	137.155	82.32	1.647	164.6	14.570%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2022-01-26T10:58:36	happy5214	Manual testing	1250000	46250000	2	7	413802557920726033831	P-1	21	68.488	0.985

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2022-01-26T10:58:36

happy5214

Manual testing

1250000

46250000

413802557920726033831

P-1

68.488

0.985

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-08T01:29:00	Will Edgington	Manual testing	?	?	15976581497	33.895	11	7.27738e-11	1.789	1.58145e-10

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-09-08T01:29:00

Will Edgington

Manual testing

15976581497

33.895

7.27738e-11

1.789

1.58145e-10

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-24T06:38:07

Oliver Kruse

GTX-2

1866715463

15976581497

F7E126B9AD3B4A__

2018-01-24T11:26:28

kkmrkkblmbrbk

old

1866715463

15976581497

F7E126B9AD3B4A__

2022-01-27T01:40:39

happy5214

Manual testing

1866715463

15976581497

413802557920726033831

468939591342953500433

F7E126B9AD3B4A3E

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 = 2500000, B2 = 6555248700 (P-1 stage 2)

B1 = 1250000, B2 = 46250000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 1250000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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