M2 944 709 Mersenne number exponent details

Residue

Status

L-L

3E941E4ACFD1385D

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁹	40.5428	68.1159%	15000000	104505841440	704.4244	17.5759%	744.9672	73.7199%
Target	2⁶³	0.5420	65.0794%	17000	1500000	0.0121	1.9470%	0.5541	65.7593%
Difference	+6	+40.0008	+3.0366%	+14983000	+104504341440	+704.4123	+15.6290%	+744.4131	+7.9606%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁹

40.5428

68.1159%

15000000

104505841440

704.4244

17.5759%

744.9672

73.7199%

Target

2⁶³

0.5420

65.0794%

17000

1500000

0.0121

1.9470%

0.5541

65.7593%

Difference

+40.0008

+3.0366%

+14983000

+104504341440

+704.4123

+15.6290%

+744.4131

+7.9606%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2944709	977421837151463968096323383	27	89.659	165962381537779109599 557303 × 1135411 × 262280003	2022-11-06	1135411	262280003	73,161,264	1.8960	3.2938
2944709	3497362970559580926461223756498259766199409	43	141.327	593838469363115494003180578539044056 2³ × 3 × 1289 × 4957 × 645083 × 4130977 × 8969647 × 162009889	2022-11-12	8969647	162009889	6.273e+10	2.1360	2.2528

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2944709

977421837151463968096323383

89.659

165962381537779109599
557303 × 1135411 × 262280003

2022-11-06

1135411

262280003

73,161,264

1.8960

3.2938

2944709

3497362970559580926461223756498259766199409

141.327

593838469363115494003180578539044056
2³ × 3 × 1289 × 4957 × 645083 × 4130977 × 8969647 × 162009889

2022-11-12

8969647

162009889

6.273e+10

2.1360

2.2528

exponent	prime factors	composite factor	digits	bits*
2944709	977421837151463968096323383 3497362970559580926461223756498259766199409	34183989398698469804859903737867311341759283529235 28380688028127480647	70	230.986

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.199%
2003-12-23	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.120%
2010-11-05	markr	tiny	105000	2310000		-		-	-	0.028	-	-	2.303%
2015-04-29	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.055%
2022-11-06	Jocelyn Larouche	Manual testing	1200000	3372218850			977421837151463968096323383	27	89.659	22.81	0.501	45.63	10.507%
2022-11-12	riccardo uberti	Xeon20C	15000000	104505841440			3497362970559580926461223756498259766199409	43	141.327	704.4	0.501	1,409	17.576%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2022-11-14	riccardo uberti	Colab_noGPU14	5000000	100000000	2	7			-	-	1.564
2022-11-15	riccardo uberti	Colab_noGPU14	5750000	120000000	6	5			-	-	1.831

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2022-11-14

riccardo uberti

Colab_noGPU14

5000000

100000000

1.564

2022-11-15

riccardo uberti

Colab_noGPU14

5750000

120000000

1.831

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13	Sturle Sunde	wright.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-24	markr	oldgamer	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.333	-	-
2015-04-27	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.667	-	-
2015-04-27	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.269	-	-
2016-02-24	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.538	-	-
2017-11-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.075	-	-
2018-12-24	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.15	-	-
2021-05-19	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.30	-	-

ECM factoring results:

Total ECM effort:	16.872 GHz-days
Estimated T-Level:	22.473

Digits	B1	Complete	FacMiss
20	11000	5.321	0.489%
25	50000	0.495	60.981%
30	250000	0.031	96.915%
35	1000000	0.001	99.853%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	95	11.00
50000	6750000	14	1.869
50000	6900000	7	0.945
50000	7000000	7	0.952
50000	14400000	10	2.109

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-31	Aca Arsov	backo6400	50000	5000000						3	0.347
2011-04-24	Martti Järvi	Tiny	50000	5000000						3	0.347
2013-07-01	Bruce	fx6840-21	50000	5000000						3	0.347
2015-12-31	Bruce	Desk7	50000	5000000						3	0.347
2017-06-03	bayanne	iMac	50000	5000000						3	0.347
2019-09-23	Yuji HASEGAWA	cfs9	50000	5000000						3	0.347
2020-09-13	LordJulius	BlackboxNouveau	50000	5000000						7	0.810
2020-10-14	daveward2005	Dave2	50000	5000000						7	0.810
2020-11-12	GAN	KA-HP	50000	5000000						7	0.810
2020-12-18	rextherunt	ice	50000	5000000						7	0.810
2021-01-18	lycorn	colab_S_1	50000	6750000						7	0.934
2021-02-20	mnd9	f4b	50000	5000000						7	0.810
2021-03-21	daveward2005	Dave2	50000	5000000						7	0.810
2021-05-06	Zenzoma	AMD3970X	50000	5000000						7	0.810
2021-06-18	LaurV	Zero818	50000	6750000						7	0.934
2021-08-03	Jonathan Webb	do-primes-2	50000	5000000						7	0.810
2021-10-08	daveward2005	Dave2	50000	5000000						7	0.810
2021-12-24	daveward2005	d12436	50000	5000000						7	0.810
2022-04-27	voidf	ATRI	50000	7000000						7	0.952
2022-08-07	daveward2005	Dave2	50000	5000000						7	0.810
2022-11-05	Alvin Bunk	BADCAT	50000	6900000						7	0.945
2022-11-12	riccardo uberti	Colab_noGPU11	50000	14400000						10	2.109

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Marco Voerman		3E941E4ACFD1385D	0.251
1999-05-09	ANONYMOUS	v4_computers	3E941E4ACFD1385D	0.251
2018-10-11	kkmrkkblmbrbk	old	3E941E4ACFD1385D	0.251

date

userid

compid

res64

spent (GHz-days)

1997-01-01

Marco Voerman

3E941E4ACFD1385D

0.251

1999-05-09

ANONYMOUS

v4_computers

3E941E4ACFD1385D

0.251

2018-10-11

kkmrkkblmbrbk

old

3E941E4ACFD1385D

0.251

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 = 15000000, B2 = 104505841440 (P-1 stage 2)

B1 = 1200000, B2 = 3372218850 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2310000 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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