M1625989 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	18.2744	68.6567%	500000	15000000	0.0835	4.9968%	18.3579	70.2229%	1.5662%
PrimeNet	2⁵⁷	0.0118	63.1579%	7000	120000	0.0009	2.5561%	0.0127	64.0996%	0.9417%
GPU72	2⁶¹	0.1889	65.5738%	6500	65000	0.0006	1.0899%	0.1895	65.9490%	0.3752%
Difference	+6	+18.0854	+3.0829%	+493500	+14935000	+0.0829	+3.9069%	+18.1684	+4.2739%	+4.2739%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.2744

68.6567%

500000

15000000

0.0835

4.9968%

18.3579

70.2229%

1.5662%

PrimeNet

2⁵⁷

0.0118

63.1579%

7000

120000

0.0009

2.5561%

0.0127

64.0996%

0.9417%

GPU72

2⁶¹

0.1889

65.5738%

6500

65000

0.0006

1.0899%

0.1895

65.9490%

0.3752%

Difference

+18.0854

+3.0829%

+493500

+14935000

+0.0829

+3.9069%

+18.1684

+4.2739%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1625989	667107514943	12	39.279	205139 11 × 17 × 1097	-	17	1097	6.317e-8	4.912e-6	7.239e-6
1625989	3055107562828863943	19	61.406	939461325639 3 × 23 × 10853 × 1254527	2015-05-02	10853	1254527	0.2420	0.0051	0.0083

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1625989

667107514943

39.279

205139
11 × 17 × 1097

1097

6.317e-8

4.912e-6

7.239e-6

1625989

3055107562828863943

61.406

939461325639
3 × 23 × 10853 × 1254527

2015-05-02

10853

1254527

0.2420

0.0051

0.0083

exponent	prime factors	composite factor	digits	bits*
1625989	667107514943 3055107562828863943	2038085214122328664206586400249	31	100.685

exponent

prime factors

composite factor

digits

bits*

1625989

667107514943
3055107562828863943

2038085214122328664206586400249

100.685

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2015-05-02T17:25:00	alpertron	Manual testing	500000	15000000	12		3055107562828863943	19	61.406	0.084	0.145	0.167	4.997%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.095 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.095 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	9.654	0.006%
25	50000	0.893	40.933%
30	250000	0.056	94.522%
35	1000000	0.003	99.737%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	14.10

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-10T22:08:39	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2018-11-19T18:25:12	rucio		50000	5000000						3	0.168
2019-11-04T17:13:48	TJAOI	Manual testing	50000	5000000						245	13.76

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T14:58:05

Oliver Kruse

GTX-1

667107514943

3055107562828863943

83E696E8548203__

2017-11-01T16:54:52

kkmrkkblmbrbk

c4.xlarge

667107514943

3055107562828863943

83E696E8548203__

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

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