M27824897 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	2⁶⁹	2.1421	63.2353%	285000	34496700	2.8844	6.8299%	5.0266	65.7463%	2.5110%
PrimeNet	2⁶⁶	0.5308	62.1212%	130000	4500000	0.4941	5.2883%	1.0248	64.1244%	2.0032%
GPU72	2⁷⁰	8.5877	64.2857%	200000	6000000	0.6926	3.9168%	9.2803	65.6846%	1.3989%
Difference	-1	-6.4455	-1.0504%	+85000	+28496700	+2.1918	+2.9131%	-4.2537	+0.0617%	+0.0617%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

2.1421

63.2353%

285000

34496700

2.8844

6.8299%

5.0266

65.7463%

2.5110%

PrimeNet

2⁶⁶

0.5308

62.1212%

130000

4500000

0.4941

5.2883%

1.0248

64.1244%

2.0032%

GPU72

2⁷⁰

8.5877

64.2857%

200000

6000000

0.6926

3.9168%

9.2803

65.6846%

1.3989%

Difference

-1

-6.4455

-1.0504%

+85000

+28496700

+2.1918

+2.9131%

-4.2537

+0.0617%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27824897	222599177	9	27.730	4 2²	-	4	4	6.432e-13	5.369e-6	1.093e-5
27824897	8180519719	10	32.930	147 3 × 7²	2008-09-08	49	49	2.122e-11	6.577e-5	0.0001
27824897	22388301674759	14	44.348	402307 402307	2008-10-01	1	402307	9.092e-8	0.0294	0.0549
27824897	4289679900335484929	19	61.896	77083482112 2¹¹ × 7³ × 13 × 23 × 367	2016-06-09	2048	2048	0.0153	0.0027	0.0056

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27824897

222599177

27.730

4
2²

6.432e-13

5.369e-6

1.093e-5

27824897

8180519719

32.930

147
3 × 7²

2008-09-08

2.122e-11

6.577e-5

0.0001

27824897

22388301674759

44.348

402307
402307

2008-10-01

402307

9.092e-8

0.0294

0.0549

27824897

4289679900335484929

61.896

77083482112
2¹¹ × 7³ × 13 × 23 × 367

2016-06-09

2048

0.0153

0.0027

0.0056

exponent	prime factors	composite factor	digits	bits*
27824897	222599177 8180519719	1820976956881671263	19	60.659
27824897	222599177 22388301674759	4983617527229075073343	22	72.078
27824897	8180519719 22388301674759	183147943325286724072721	24	77.277
27824897	222599177 4289679900335484929	954879215408120969091303433	27	89.625
27824897	8180519719 4289679900335484929	35091811012892389177111814951	29	94.825
27824897	222599177 8180519719 22388301674759	40768581453451468067613782750617	32	105.007
27824897	22388301674759 4289679900335484929	96038647696860957441887104207111	32	106.243
27824897	222599177 8180519719 4289679900335484929	7811408250909382220388797245068895327	37	122.555
27824897	222599177 22388301674759 4289679900335484929	21378123937514194609996094723416146147647	41	133.973
27824897	8180519719 22388301674759 4289679900335484929	785646051270264996754577252538079395521809	42	139.173
27824897	222599177 8180519719 22388301674759 4289679900335484929	17488416442606079284947656739789763460381216895119 3	51	166.903

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-05-21T03:33:30	masser	Manual testing	285000	34496700		-	skipped known factor: 222599177 skipped known factor: 8180519719 skipped known factor: 22388301674759 skipped known factor: 4289679900335484929	-	-	2.884	-	-	6.830%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-10-01T01:55:00	markr	Manual testing	?	?	22388301674759	44.348	14	6.69074e-9	53.03	1.37760e-8
2008-09-08T23:37:00	Will Edgington	Manual testing	?	?	8180519719	32.930	10	6.54283e-13	53.03	1.34715e-12
2016-06-09T16:47:21	TJAOI	Manual testing	2⁶¹	2⁶²*	4289679900335484929	61.896	19	0.004	53.01	0.009
2022-08-10T19:29:00	LordJulius	Manual testing	2¹	2⁶⁵	222599177 8180519719	60.659	19	0.006	53.02	0.012
2022-08-10T19:29:00	LordJulius	Manual testing	2¹	2⁶⁵	222599177	27.730	9	6.43155e-13	53.03	1.32424e-12
2022-08-10T19:29:00	LordJulius	Manual testing	2¹	2⁶⁵	22388301674759	44.348	14	9.09175e-8	53.03	1.87196e-7
2022-08-10T19:29:00	LordJulius	Manual testing	2¹	2⁶⁵	4289679900335484929	61.896	19	0.015	53.01	0.032
2022-08-10T19:29:00	LordJulius	Manual testing	2¹	2⁶⁵	8180519719	32.930	10	2.12174e-11	53.03	4.36861e-11
2022-08-10T19:29:01	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.269	-	-
2022-08-10T19:29:01	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.537	-	-
2022-08-10T19:29:01	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.074	-	-
2022-08-05T12:41:58	masser	Manual testing	2⁶⁷	2⁶⁹		-	-	3.223	-	-

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 = 285000, B2 = 34496700 (P-1 stage 2)

B1 = 285000 (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