M4 371 529 Mersenne number exponent details

Residue

Status

L-L

A1944D3895AFBCD1

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	218.7641	68.0556%	6200000	32756371830	323.8105	12.8360%	542.5746	72.1559%
Target	2⁶⁵	1.6689	64.6154%	24000	2500000	0.0287	1.9876%	1.6976	65.3187%
Difference	+7	+217.0952	+3.4402%	+6176000	+32753871830	+323.7818	+10.8484%	+540.8770	+6.8373%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

218.7641

68.0556%

6200000

32756371830

323.8105

12.8360%

542.5746

72.1559%

Target

2⁶⁵

1.6689

64.6154%

24000

2500000

0.0287

1.9876%

1.6976

65.3187%

Difference

+217.0952

+3.4402%

+6176000

+32753871830

+323.7818

+10.8484%

+540.8770

+6.8373%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4371529	1176824450956376469831848154080930670593713	43	139.756	134601011563274139303645035190311064 2³ × 3 × 7 × 9241 × 14951 × 15101 × 330821 × 2734817 × 424446329	2022-12-18	2734817	424446329	4.031e+10	4.6497	7.8110

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4371529

1176824450956376469831848154080930670593713

139.756

134601011563274139303645035190311064
2³ × 3 × 7 × 9241 × 14951 × 15101 × 330821 × 2734817 × 424446329

2022-12-18

2734817

424446329

4.031e+10

4.6497

7.8110

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-05	Carsten Kossendey	durandal	25000	356250		-		-	-	0.008	-	-	0.661%
2012-01-04	Squeeky_Squirrel	T7500_2200	110000	2255000		-		-	-	0.041	-	-	1.709%
2018-10-26	Ismo Laitela	6600K	2189464	63494458	12	-		-	-	1.000	-	-	5.381%
2022-12-18	DRobinsonPE	5800X	6200000	32756371830			1176824450956376469831848154080930670593713	43	139.756	323.8	1.090	647.6	12.836%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-01	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.070	-	-
2010-11-16	markr	ut	2⁶¹	2⁶²		-	-	0.070	-	-
2012-02-10	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.365	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.225	-	-
2014-07-12	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.449	-	-
2014-07-12	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.855	-	-
2015-06-18	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.709	-	-
2018-05-03	chuenkit	Manual testing	2⁶⁶	2⁶⁷		-	-	3.419	-	-
2018-10-29	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	6.838	-	-
2021-01-25	-Anonymous-	Manual testing	2⁶⁸	2⁶⁹		-	-	13.68	-	-
2021-01-25	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	27.35	-	-
2021-01-31	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	54.70	-	-
2021-01-31	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	109.4	-	-

ECM factoring results:

Total ECM effort:	2.202 GHz-days
Estimated T-Level:	2.308

Digits	B1	Complete	FacMiss
20	11000	0.462	63.031%
25	50000	0.043	95.819%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	2.202

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-21	oodaira	Win02	50000	5000000						3	0.551
2013-05-29	ANONYMOUS		50000	5000000						3	0.551
2016-08-22	bayanne	iMac	50000	5000000						3	0.551
2019-07-06	furkell	furkell1	50000	5000000						3	0.551

date	userid	compid	res64	spent (GHz-days)
1998-11-21	ANONYMOUS	v4_computers	A1944D3895AFBCD1	0.545
1999-10-29	ANONYMOUS	v4_computers	A1944D3895AFBCD1	0.545

date

userid

compid

res64

spent (GHz-days)

1998-11-21

ANONYMOUS

v4_computers

A1944D3895AFBCD1

0.545

1999-10-29

ANONYMOUS

v4_computers

A1944D3895AFBCD1

0.545

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 = 6200000, B2 = 32756371830 (P-1 stage 2)

B1 = 6200000 (P-1 stage 1)

B1 = 2189464, B2 = 63494458 (P-1 stage 2)

B1 = 2189464 (P-1 stage 1)

B1 = 110000, B2 = 2255000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 25000, B2 = 356250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 65

TF double-checked to: 67.9

ECM T-Level=2.31 ~= -9-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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