M1915241 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	15.5145	68.6567%	500000	15000000	0.1015	5.0964%	15.6159	70.2541%	1.5974%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0914%	0.0114	64.2968%	1.1389%
GPU72	2⁶¹	0.1604	65.5738%	10000	170000	0.0015	1.7607%	0.1619	66.1799%	0.6061%
Difference	+6	+15.3541	+3.0829%	+490000	+14830000	+0.1000	+3.3358%	+15.4541	+4.0742%	+4.0742%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.5145

68.6567%

500000

15000000

0.1015

5.0964%

15.6159

70.2541%

1.5974%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0914%

0.0114

64.2968%

1.1389%

GPU72

2⁶¹

0.1604

65.5738%

10000

170000

0.0015

1.7607%

0.1619

66.1799%

0.6061%

Difference

+15.3541

+3.0829%

+490000

+14830000

+0.1000

+3.3358%

+15.4541

+4.0742%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1915241	27192591719	11	34.662	7099 31 × 229	-	31	229	1.836e-9	3.287e-6	4.963e-6
1915241	318217039290655548863	21	68.109	83074933987591 7 × 13 × 61 × 14965760041	2021-04-22	61	14965760041	37.411	64.140	119.79

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1915241

27192591719

34.662

7099
31 × 229

229

1.836e-9

3.287e-6

4.963e-6

1915241

318217039290655548863

68.109

83074933987591
7 × 13 × 61 × 14965760041

2021-04-22

14965760041

37.411

64.140

119.79

exponent	prime factors	composite factor	digits	bits*
1915241	27192591719 318217039290655548863	8653146027459777712093413665497	31	102.771

exponent

prime factors

composite factor

digits

bits*

1915241

27192591719
318217039290655548863

8653146027459777712093413665497

102.771

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:42:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 27192591719	-	-	0.101	-	-	5.096%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:42:25

alpertron

Manual testing

500000

15000000

skipped known factor: 27192591719

0.101

-

-

5.096%

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.811 GHz-days
Estimated T-Level:	24.571

Digits	B1	Curves	Complete	FacMiss
20	11000	256 / 100	2.560	7.631%
25	50000	256 / 280	0.914	40.015%

New Calculation Method

Total ECM effort:	21.811 GHz-days
Estimated T-Level:	24.571

Digits	B1	Complete	FacMiss
20	11000	9.065	0.012%
25	50000	0.804	44.754%
30	250000	0.050	95.140%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		7	0.293
50000	5000000		20	1.389
50000	6156523		14	1.062
50000	6750000		7	0.554
50000	6750000	318217039290655548863	1	0.079
50000	8000000		214	18.43

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T18:11:58	alpertron		50000	5000000						3	0.208
2018-09-28T16:55:00	alpertron	Manual testing	50000	5000000						3	0.208
2020-10-28T18:48:45	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2021-01-19T16:45:37	seatsea	dt	50000	6156523						7	0.531
2021-04-22T20:14:42	nordi	sweet16	50000	6750000	318217039290655548863	68.109	1	2	7677641599139612	1	0.079
2021-05-09T01:17:38	nordi	sweet16	50000	6750000						7	0.554
2021-07-14T09:01:40	seatsea	Manual testing	50000	6156523						7	0.531
2021-11-29T01:24:31	JackBlock	school2	50000	50000						7	0.293
2021-12-15T07:08:50	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2022-01-18T14:10:46	TJAOI	Manual testing	50000	8000000						214	18.43

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:14:47

alpertron

Manual testing

27192591719

369C3E95AB1E8E__

2017-10-20T04:31:30

Oliver Kruse

Threadripper

27192591719

369C3E95AB1E8E__

2021-04-22T21:41:22

mikr

Nitron

27192591719

318217039290655548863

15C3D25F20BC155C

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

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