M5214613 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	5.6982	65.6716%	2500000	6555248700	82.3207	14.5700%	88.0189	70.6733%	5.0016%
PrimeNet	2⁶²	0.1178	62.9032%	22000	500000	0.0110	3.0042%	0.1288	64.0177%	1.1145%
GPU72	2⁶⁶	2.8321	65.1515%	30000	600000	0.0140	1.9882%	2.8461	65.8444%	0.6928%
Difference	+1	+2.8661	+0.5201%	+2470000	+6554648700	+82.3067	+12.5818%	+85.1728	+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

5.6982

65.6716%

2500000

6555248700

82.3207

14.5700%

88.0189

70.6733%

5.0016%

PrimeNet

2⁶²

0.1178

62.9032%

22000

500000

0.0110

3.0042%

0.1288

64.0177%

1.1145%

GPU72

2⁶⁶

2.8321

65.1515%

30000

600000

0.0140

1.9882%

2.8461

65.8444%

0.6928%

Difference

+2.8661

+0.5201%

+2470000

+6554648700

+82.3067

+12.5818%

+85.1728

+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
5214613	53063901889	11	35.627	5088 2⁵ × 3 × 53	-	32	53	9.667e-10	7.589e-6	1.491e-5
5214613	172818041192661621641	21	67.228	16570552905140 2² × 5 × 13 × 37 × 1722510697	2022-01-13	37	1722510697	5.7975	21.489	40.136
5214613	694544760018355686903098617	27	89.166	66596002428018693516 2² × 3 × 167 × 1709 × 2551 × 26053 × 292577	2022-01-28	26053	292577	35,470,334	0.0093	0.0121

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5214613

53063901889

35.627

5088
2⁵ × 3 × 53

9.667e-10

7.589e-6

1.491e-5

5214613

172818041192661621641

67.228

16570552905140
2² × 5 × 13 × 37 × 1722510697

2022-01-13

1722510697

5.7975

21.489

40.136

5214613

694544760018355686903098617

89.166

66596002428018693516
2² × 3 × 167 × 1709 × 2551 × 26053 × 292577

2022-01-28

26053

292577

35,470,334

0.0093

0.0121

exponent	prime factors	composite factor	digits	bits*
5214613	53063901889 172818041192661621641	9170399582496556837533663179849	31	102.855
5214613	53063901889 694544760018355686903098617	36855255003133076008931227262579587513	38	124.793
5214613	172818041192661621641 694544760018355686903098617	120029864946999473619198447384834741778964370497	48	156.394
5214613	53063901889 172818041192661621641 694544760018355686903098617	63692529772975002530637901588499993642376146800794 54168833	58	192.021

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-28T06:25:43	happy5214	Manual testing	2500000	2500000			694544760018355686903098617	27	89.166	0.572	1.647	1.145	4.119%
2022-01-30T00:04:23	happy5214	Manual testing	2500000	6555248700		-	skipped known factor: 53063901889 skipped known factor: 172818041192661621641 skipped known factor: 694544760018355686903098617	-	-	82.32	-	-	14.570%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-01-28T06:25:43	happy5214	Manual testing	1250000	1250000	2	7	694544760018355686903098617	P-1	27	89.166	0.435
2022-01-30T00:04:23	happy5214	Manual testing	1250000	45000000	6	5			-	-	0.970
2022-01-30T01:03:27	happy5214	Manual testing	1250000	46250000	2	7			-	-	0.985

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-01-13T11:37:51	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	172818041192661621641	67.228	21	0.099	1.672	0.201

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-24T06:45:25

Oliver Kruse

GTX-1

53063901889

2704179B23D6D6__

2018-01-22T15:28:09

kkmrkkblmbrbk

c4.xlarge

53063901889

2704179B23D6D6__

2022-01-19T17:39:52

Team_Inspector

Purple

53063901889

172818041192661621641

2704179B23D6D6EB

2022-01-28T12:31:56

happy5214

Manual testing

53063901889

172818041192661621641

694544760018355686903098617

2704179B23D6D6EB

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 = 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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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