M110 459 903 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	2⁷⁷	277.0975	64.9351%	764000	22672000	12.4580	3.6281%	289.5555	66.2073%
Target	2⁷⁶	138.5480	64.4737%	700000	26000000	13.2268	4.0499%	151.7748	65.9125%
Difference	+1	+138.5496	+0.4614%	+64000	-3328000	-0.7688	-0.4218%	+137.7808	+0.2948%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁷

277.0975

64.9351%

764000

22672000

12.4580

3.6281%

289.5555

66.2073%

Target

2⁷⁶

138.5480

64.4737%

700000

26000000

13.2268

4.0499%

151.7748

65.9125%

Difference

+138.5496

+0.4614%

+64000

-3328000

-0.7688

-0.4218%

+137.7808

+0.2948%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
110459903	1410810295500596235190529	25	80.223	6386074300194688 2⁷ × 11² × 13877 × 29712763	2022-03-14	13877	29712763	2,892.4	10.386	19.241

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

110459903

1410810295500596235190529

80.223

6386074300194688
2⁷ × 11² × 13877 × 29712763

2022-03-14

13877

29712763

2,892.4

10.386

19.241

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-03-08	JacobZ	MServer	764000	22672000	12		1410810295500596235190529	25	80.223	12.46	969.6	24.92	3.628%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2010-05-05	EPF		2⁶³	2⁶⁴		-	-	0.018	-	-
2010-09-18	sasaki3	mate24	2⁶⁴	2⁶⁵		-	-	0.034	-	-
2012-05-26	tsc	pdm	2⁶⁵	2⁶⁶		-	-	0.068	-	-
2013-09-30	ANONYMOUS	Manual testing	2⁶⁶	2⁶⁷		-	-	0.135	-	-
2013-09-30	instant28	Manual testing	2⁶⁶	2⁶⁷		-	-	0.135	-	-
2013-10-01	instant28	Manual testing	2⁶⁷	2⁶⁸		-	-	0.271	-	-
2013-10-01	instant28	Manual testing	2⁶⁸	2⁶⁹		-	-	0.541	-	-
2014-06-23	Andreas_Truetsch	Manual testing	2⁶⁹	2⁷⁰		-	-	1.082	-	-
2014-07-30	Helmut Kirrmaier	X4170RH5226	2⁷⁰	2⁷¹		-	-	2.165	-	-
2019-01-23	Niels_Mache_Nextcloud	Manual testing	2⁷¹	2⁷²		-	-	4.330	-	-
2020-05-05	GROBERTS	Manual testing	2⁷²	2⁷³		-	-	8.659	-	-
2020-07-30	TheGazMan	Manual testing	2⁷³	2⁷⁴		-	-	17.32	-	-
2021-05-07	TheJudger	Manual testing	2⁷⁴	2⁷⁵		-	-	34.64	-	-
2021-05-07	TheJudger	Manual testing	2⁷⁵	2⁷⁶		-	-	69.27	-	-
2022-01-23	David Hruska	Manual testing	2⁷⁶	2⁷⁷		-	-	138.5	-	-

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 = 764000, B2 = 22672000 (P-1 stage 2)

B1 = 764000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁷

2⁷⁶

2⁷⁵

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

this exponent TF target: 76

TF double-checked to: 67.7

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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