M2 209 001 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
Actual	2⁶⁷	13.4513	67.1642%	500000	15000000	0.1230	5.1846%	13.5743	68.8666%
Target	2⁶²	0.2781	64.5161%	11000	850000	0.0054	1.6013%	0.2835	65.0843%
Difference	+5	+13.1732	+2.6481%	+489000	+14150000	+0.1176	+3.5833%	+13.2908	+3.7822%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

13.4513

67.1642%

500000

15000000

0.1230

5.1846%

13.5743

68.8666%

Target

2⁶²

0.2781

64.5161%

11000

850000

0.0054

1.6013%

0.2835

65.0843%

Difference

+13.1732

+2.6481%

+489000

+14150000

+0.1176

+3.5833%

+13.2908

+3.7822%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2209001	278334127	9	28.052	63 3² × 7	-	9	9	1.641e-11	8.580e-7	1.746e-6
2209001	2558023159	10	31.252	579 3 × 193	2008-07-14	3	193	1.457e-10	1.273e-6	1.904e-6
2209001	4401209174399	13	42.001	996199 23 × 43313	2008-07-14	23	43313	4.317e-7	0.0002	0.0004
2209001	19450818854533144151	20	64.076	4402627897075 5² × 176105115883	2017-07-11	25	176105115883	2.0708	914.73	1,708.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2209001

278334127

28.052

63
3² × 7

1.641e-11

8.580e-7

1.746e-6

2209001

2558023159

31.252

579
3 × 193

2008-07-14

193

1.457e-10

1.273e-6

1.904e-6

2209001

4401209174399

42.001

996199
23 × 43313

2008-07-14

43313

4.317e-7

0.0002

0.0004

2209001

19450818854533144151

64.076

4402627897075
5² × 176105115883

2017-07-11

176105115883

2.0708

914.73

1,708.5

exponent	prime factors	composite factor	digits	bits*
2209001	278334127 2558023159	711985142806047193	18	59.305
2209001	278334127 4401209174399	1225006713300736414673	22	70.053
2209001	2558023159 4401209174399	11258394995715911906441	23	73.253
2209001	278334127 19450818854533144151	5413826685311622669833741177	28	92.129
2209001	2558023159 19450818854533144151	49755645091409634871343393009	29	95.329
2209001	278334127 2558023159 4401209174399	3133595542553757080488161412007	31	101.306
2209001	4401209174399 19450818854533144151	85607122392144322247404365790249	32	106.078
2209001	278334127 2558023159 19450818854533144151	13848694039839335921304120610377918143	38	123.381
2209001	278334127 4401209174399 19450818854533144151	23827383675999641590737972168217620527623	41	134.130
2209001	2558023159 4401209174399 19450818854533144151	218985001654452655979219295329164278376591	42	137.330
2209001	278334127 2558023159 4401209174399 19450818854533144151	60950999261585635664807332706998117061533433221057	50	165.382

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-04-17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 278334127 skipped known factor: 2558023159 skipped known factor: 4401209174399	-	-	0.123	-	-	5.185%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-07-11	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	19450818854533144151	64.076	20	0.459	0.292	0.925

ECM factoring results:

Total ECM effort:	7.799 GHz-days
Estimated T-Level:	21.527

Digits	B1	Complete	FacMiss
20	11000	3.282	3.755%
25	50000	0.305	73.686%
30	250000	0.019	98.077%

ECM Summary

B1	B2	factor	curves	GHz-days
		2558023159	1	0.00000e+0
		4401209174399	1	0.00000e+0
50000	5000000		3	0.257
50000	6750000		7	0.686
50000	6844787		7	0.691
50000	6900000		48	4.755
50000	7135637		7	0.705
50000	7150000		7	0.706

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14	George Woltman	Manual testing			4401209174399	42.001		1		1	-
2008-07-14	George Woltman	Manual testing			2558023159	31.252		1		1	-
2018-01-18	Oliver Kruse	ECM-HTC	50000	5000000						3	0.257
2022-05-18	Dylan Delgado	laptop-i78750	50000	6750000						7	0.686
2022-07-15	debrouxl	athlon2	50000	7150000						7	0.706
2022-09-27	debrouxl	o9020	50000	6844787						7	0.691
2022-12-01	kracker	O0	50000	7135637						7	0.705
2023-06-10	debrouxl	x8dtt-h-f	50000	6900000						48	4.755

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28

alpertron

Manual testing

278334127

2558023159

4401209174399

19450818854533144151

19D47B20326E27__

2017-10-25

Oliver Kruse

GTX-0

278334127

2558023159

4401209174399

19450818854533144151

19D47B20326E27__

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

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