M1849733 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	16.0639	68.6567%	500100	500100	0.0393	1.9983%	16.1032	69.2830%	0.6263%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0230%	0.0117	64.2716%	1.1137%
GPU72	2⁶¹	0.1661	65.5738%	9000	150000	0.0013	1.6309%	0.1674	66.1352%	0.5615%
Difference	+6	+15.8978	+3.0829%	+491100	+350100	+0.0380	+0.3673%	+15.9359	+3.1478%	+3.1478%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0639

68.6567%

500100

0.0393

1.9983%

16.1032

69.2830%

0.6263%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0230%

0.0117

64.2716%

1.1137%

GPU72

2⁶¹

0.1661

65.5738%

9000

150000

0.0013

1.6309%

0.1674

66.1352%

0.5615%

Difference

+15.8978

+3.0829%

+491100

+350100

+0.0380

+0.3673%

+15.9359

+3.1478%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1849733	55491991	8	25.726	15 3 × 5	-	3	5	2.424e-12	2.446e-7	4.803e-7
1849733	23855759271957814871	20	64.371	6448433171695 5 × 17 × 109 × 695999263	2017-09-21	109	695999263	3.4960	2.9829	5.5712
1849733	164741620587220705687	21	67.159	44531189254671 3 × 7 × 17 × 4007 × 31129829	2021-03-28	4007	31129829	31.562	0.1337	0.2492

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1849733

55491991

25.726

15
3 × 5

2.424e-12

2.446e-7

4.803e-7

1849733

23855759271957814871

64.371

6448433171695
5 × 17 × 109 × 695999263

2017-09-21

109

695999263

3.4960

2.9829

5.5712

1849733

164741620587220705687

67.159

44531189254671
3 × 7 × 17 × 4007 × 31129829

2021-03-28

4007

31129829

31.562

0.1337

0.2492

exponent	prime factors	composite factor	digits	bits*
1849733	55491991 23855759271957814871	1323803578817649615201198161	28	90.097
1849733	55491991 164741620587220705687	9141840526951466114996652817	28	92.885
1849733	23855759271957814871 164741620587220705687	3930036442800946787886892418643122871377	40	131.530
1849733	55491991 23855759271957814871 164741620587220705687	218085546913582153944898343113312406590346641607	48	157.256

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-04-12T11:56:57	Lisander Viaene	Desktop	500100	500100		-	skipped known factor: 55491991	-	-	0.039	-	-	1.998%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-04-12T11:56:57

Lisander Viaene

Desktop

500100

skipped known factor: 55491991

0.039

-

-

1.998%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2017-09-21T11:31:00	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	23855759271957814871	64.371	20	1.572	0.204	3.196

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2017-09-21T11:31:00

TJAOI

Manual testing

2⁶⁴

2⁶⁵*

23855759271957814871

64.371

1.572

0.204

3.196

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.800 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.800 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.816	0.015%
25	50000	0.799	44.991%
30	250000	0.049	95.179%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.005
50000	5000000	164741620587220705687	7	0.484
50000	6600000		222	17.31

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T14:15:16	Gordon Spence	haswell	50000	5000000						3	0.207
2019-01-14T03:36:52	ATH	ec2-ECMCF	50000	5000000						3	0.207
2020-06-15T04:34:58	nordi	sweet16	50000	5000000						3	0.207
2020-07-11T01:12:34	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-08-13T05:20:56	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-10-15T22:05:20	MarkS	desktop-i7	50000	5000000						7	0.484
2020-12-29T15:54:10	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.484
2021-03-28T02:24:59	MarkS	desktop-i7	50000	5000000	164741620587220705687	67.159	7	2	616234865198640	7	0.484
2021-07-09T11:25:05	TJAOI	Manual testing	50000	6600000						222	17.31

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T06:12:28

Oliver Kruse

GTX-0

55491991

23855759271957814871

2FB883E4AD03FA__

2017-11-06T22:48:51

kkmrkkblmbrbk

c4.xlarge

55491991

23855759271957814871

2FB883E4AD03FA__

2021-03-28T20:43:10

rbanov

ccg_lnx02

55491991

23855759271957814871

164741620587220705687

EE46822ED443F41E

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 = 500100 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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