M3152189 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	2⁶⁹	37.8743	68.1159%	1000000	119912100	0.9229	6.8712%	38.7972	70.3068%	2.1908%
PrimeNet	2⁶⁰	0.0487	63.3333%	13000	240000	0.0031	2.6502%	0.0519	64.3051%	0.9717%
GPU72	2⁶⁴	1.1292	65.6250%	15000	240000	0.0034	1.5444%	1.1325	66.1559%	0.5309%
Difference	+5	+36.7451	+2.4909%	+985000	+119672100	+0.9196	+5.3268%	+37.6647	+4.1509%	+4.1509%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

37.8743

68.1159%

1000000

119912100

0.9229

6.8712%

38.7972

70.3068%

2.1908%

PrimeNet

2⁶⁰

0.0487

63.3333%

13000

240000

0.0031

2.6502%

0.0519

64.3051%

0.9717%

GPU72

2⁶⁴

1.1292

65.6250%

15000

240000

0.0034

1.5444%

1.1325

66.1559%

0.5309%

Difference

+36.7451

+2.4909%

+985000

+119672100

+0.9196

+5.3268%

+37.6647

+4.1509%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3152189	1462615697	10	30.446	232 2³ × 29	-	8	29	4.766e-11	1.128e-6	2.009e-6
3152189	229891457937695814983	21	67.640	36465367073119 31 × 1176302163649	2021-04-19	31	1176302163649	18.086	7,909.2	14,772

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3152189

1462615697

30.446

232
2³ × 29

4.766e-11

1.128e-6

2.009e-6

3152189

229891457937695814983

67.640

36465367073119
31 × 1176302163649

2021-04-19

1176302163649

18.086

7,909.2

14,772

exponent	prime factors	composite factor	digits	bits*
3152189	1462615697 229891457937695814983	336242854985889147005343588151	30	98.085

exponent

prime factors

composite factor

digits

bits*

3152189

1462615697
229891457937695814983

336242854985889147005343588151

98.085

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-04T08:51:21	Jocelyn Larouche	Manual testing	315218	315218		-	skipped known factor: 1462615697	-	-	0.039	-	-	1.383%
2021-01-04T13:51:17	Jocelyn Larouche	Manual testing	315218	3152189	6	-	skipped known factor: 1462615697	-	-	0.058	-	-	3.003%
2022-02-12T07:46:36	Jocelyn Larouche	Manual testing	1000000	119912100		-	skipped known factor: 1462615697	-	-	0.923	-	-	6.871%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-01-04T08:51:24	Jocelyn Larouche	Manual testing	2⁵⁹	2⁶⁰		-	-	0.024	-	-
2021-01-04T09:13:18	Jocelyn Larouche	Manual testing	2⁶⁰	2⁶¹		-	-	0.049	-	-
2021-01-04T15:32:55	Jocelyn Larouche	Manual testing	2⁶¹	2⁶²		-	-	0.097	-	-
2021-01-05T11:55:20	Jocelyn Larouche	Manual testing	2⁶²	2⁶³		-	-	0.311	-	-
2021-01-06T20:01:32	Jocelyn Larouche	Manual testing	2⁶³	2⁶⁴		-	-	0.623	-	-
2021-01-09T20:29:15	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵		-	-	1.185	-	-
2022-03-24T17:59:09	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.371	-	-
2022-03-24T17:59:09	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.741	-	-
2021-04-19T19:07:18	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸	229891457937695814983	67.640	21	8.660	0.545	17.58
2021-12-06T01:55:29	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.97	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.351 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.351 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.351

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-08-10T02:24:03	ATH	ec2-ECMCF	50000	5000000						3	0.351

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-30T22:59:13

Oliver Kruse

GTX-0

1462615697

EBFBAC28EA9DA2__

2017-12-12T14:21:37

kkmrkkblmbrbk

c4.xlarge

1462615697

EBFBAC28EA9DA2__

2021-04-20T13:31:03

marssystems

system11

1462615697

229891457937695814983

EBFBAC28EA9DA208

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 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 315218, B2 = 3152189 (P-1 stage 2)

B1 = 315218 (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