M4 294 967 291 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	2⁸⁴	912.1996	61.9048%	-	-	-	-	912.1996	61.9048%
Target	2⁹²	233,523.1183	65.2174%	22000000	1300000000	35,960.3920	4.3567%	269,483.5103	66.7328%
Difference	-8	-232,610.9187	-3.3126%	-22000000	-1300000000	-35,960.3920	-4.3567%	-268,571.3107	-4.8280%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁸⁴

912.1996

61.9048%

912.1996

61.9048%

Target

2⁹²

233,523.1183

65.2174%

22000000

1300000000

35,960.3920

4.3567%

269,483.5103

66.7328%

Difference

-8

-232,610.9187

-3.3126%

-22000000

-1300000000

-35,960.3920

-4.3567%

-268,571.3107

-4.8280%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4294967291	8589934583	10	33.000	1 1	2012-08-20	1	1	1.335e-13	0.0004	0.0008
4294967291	104088783547645764059161	24	76.462	12117529249380 2² × 3² × 5 × 139 × 484313719	2017-08-19	139	484313719	5.5994	10,356	19,341

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4294967291

8589934583

33.000

1
1

2012-08-20

1.335e-13

0.0004

0.0008

4294967291

104088783547645764059161

76.462

12117529249380
2² × 3² × 5 × 139 × 484313719

2017-08-19

139

484313719

5.5994

10,356

19,341

exponent	prime factors	composite factor	digits	bits*
4294967291	8589934583 104088783547645764059161	894115841498323776925245531864863	33	109.462

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2020-05-11	ramgeis	r4mg31s	2¹	2⁶⁹	8589934583	33.000	10	0.028	2,363,790	0.911
2022-05-02	LordJulius	WhiteBox	2¹	2⁷³	8589934583	33.000	10	0.445	2,363,790	0.911
2023-02-09	Dobri	MaiPenRai	2¹	2⁷³	8589934583	33.000	10	0.445	2,363,790	0.911
2022-12-02	LordJulius	WhiteBox	2⁷³	2⁷⁴		-	-	0.445	-	-
2023-02-09	Dobri	MaiPenRai	2⁷³	2⁷⁴		-	-	0.445	-	-
2022-12-02	LordJulius	WhiteBox	2⁷⁴	2⁷⁵		-	-	0.891	-	-
2023-02-09	Dobri	MaiPenRai	2⁷⁴	2⁷⁵		-	-	0.891	-	-
2017-08-19			2⁷⁵	2⁷⁶		-	-	1.782	-	-
2023-02-09	Dobri	MaiPenRai	2⁷⁵	2⁷⁶		-	-	1.782	-	-
2017-08-19			2⁷⁶	2⁷⁷	104088783547645764059161	76.462	24	3.101	2,363,790	7.290
2023-02-09	Dobri	MaiPenRai	2⁷⁶	2⁷⁷	104088783547645764059161	76.462	24	3.563	2,363,790	7.290
2017-08-19			2⁷⁷	2⁷⁸		-	-	7.127	-	-
2017-08-19			2⁷⁸	2⁷⁹		-	-	14.25	-	-
2017-08-19			2⁷⁹	2⁸⁰		-	-	28.51	-	-
2021-11-17	kriesel	test-gtx1080ti	2⁸⁰	2⁸¹		-	-	57.01	-	-
2021-11-17	kriesel	test-gtx1080ti	2⁸¹	2⁸²		-	-	114.0	-	-
2023-02-10	Dobri	MaiPenRai	2⁸²	2⁸³		-	-	228.1	-	-
2023-02-10	Kriesel	dodo-rtx2080super	2⁸²	2⁸³		-	-	228.1	-	-
2023-02-10	Kriesel	dodo-rtx2080super	2⁸³	2⁸⁴		-	-	456.1	-	-

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

10⁰

10¹

10²

10³

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