M2053069 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	14.4729	68.6567%	500000	15000000	0.1230	5.1392%	14.5959	70.2675%	1.6108%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6664%	0.0203	64.7585%	0.9654%
GPU72	2⁶²	0.2992	66.1290%	9000	120000	0.0014	1.3307%	0.3007	66.5798%	0.4507%
Difference	+5	+14.1737	+2.5277%	+491000	+14880000	+0.1216	+3.8085%	+14.2952	+3.6878%	+3.6878%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.4729

68.6567%

500000

15000000

0.1230

5.1392%

14.5959

70.2675%

1.6108%

PrimeNet

2⁵⁸

0.0187

63.7931%

9000

160000

0.0016

2.6664%

0.0203

64.7585%

0.9654%

GPU72

2⁶²

0.2992

66.1290%

9000

120000

0.0014

1.3307%

0.3007

66.5798%

0.4507%

Difference

+14.1737

+2.5277%

+491000

+14880000

+0.1216

+3.8085%

+14.2952

+3.6878%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2053069	229943729	9	27.777	56 2³ × 7	-	8	8	8.815e-12	7.627e-7	1.552e-6
2053069	61644804973719986605508807479127	32	105.604	15012842961858560673194327 13² × 541951 × 163914062907634433	2022-06-03	541951	163914062907634433	9.371e+10	851,410,621	1.590e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2053069

229943729

27.777

56
2³ × 7

8.815e-12

7.627e-7

1.552e-6

2053069

61644804973719986605508807479127

105.604

15012842961858560673194327
13² × 541951 × 163914062907634433

2022-06-03

541951

163914062907634433

9.371e+10

851,410,621

1.590e+9

exponent	prime factors	composite factor	digits	bits*
2053069	229943729 61644804973719986605508807479127	14174836329134920721900747134093552044583	41	133.380

exponent

prime factors

composite factor

digits

bits*

2053069

229943729
61644804973719986605508807479127

14174836329134920721900747134093552044583

133.380

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:20:09	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 229943729	-	-	0.123	-	-	5.139%

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.175 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	3.175 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.413	24.330%
25	50000	0.131	87.724%
30	250000	0.008	99.176%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.291
50000	6900000	61644804973719986605508807479127	2	0.196
50000	6947783		7	0.688

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-30T09:05:17	ATH	ec2-1xe	50000	5000000						3	0.255
2019-07-15T02:45:59	MarkS	laptop64	50000	5000000						3	0.255
2021-07-25T12:00:14	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.594
2021-10-11T19:09:37	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.594
2022-03-01T16:32:35	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.594
2022-06-03T03:24:27	debrouxl	dl380g9-1	50000	6900000	61644804973719986605508807479127	105.604	2	2	2266466507698825	2	0.196
2022-06-21T02:43:52	debrouxl	o9020	50000	6947783						7	0.688

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T08:53:12

Oliver Kruse

GTX-1

229943729

097ED659BC8A04__

2017-11-15T15:56:03

Chang Chia-Tche

exbpc13

229943729

097ED659BC8A04__

2022-06-08T23:45:52

XZT

600G2Mini1

229943729

61644804973719986605508807479127

24D2636086E77F__

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

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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