M3754259 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

A1FF3C23880A4BB9

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	63.6479	68.5714%	1600000	66000000	0.7780	6.1494%	64.4259	70.5041%	1.9327%
PrimeNet	2⁶⁰	0.0409	63.3333%	16000	320000	0.0050	3.0914%	0.0459	64.4669%	1.1335%
GPU72	2⁶⁴	0.9481	65.6250%	22000	450000	0.0069	2.1111%	0.9550	66.3507%	0.7257%
Difference	+6	+62.6998	+2.9464%	+1578000	+65550000	+0.7711	+4.0383%	+63.4709	+4.1534%	+4.1534%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

63.6479

68.5714%

1600000

66000000

0.7780

6.1494%

64.4259

70.5041%

1.9327%

PrimeNet

2⁶⁰

0.0409

63.3333%

16000

320000

0.0050

3.0914%

0.0459

64.4669%

1.1335%

GPU72

2⁶⁴

0.9481

65.6250%

22000

450000

0.0069

2.1111%

0.9550

66.3507%

0.7257%

Difference

+62.6998

+2.9464%

+1578000

+65550000

+0.7711

+4.0383%

+63.4709

+4.1534%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3754259	41968023079268567115719	23	75.152	5589388355900401 13 × 1439 × 298785928043	2021-10-30	1439	298785928043	3,997.5	2,479.1	4,630.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3754259

41968023079268567115719

75.152

5589388355900401
13 × 1439 × 298785928043

2021-10-30

1439

298785928043

3,997.5

2,479.1

4,630.2

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T17:50:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.730%
2013-03-17T20:39:00	Squeeky_Squirrel	P4_2600	110000	2035000		-		-	-	0.033	-	-	2.076%
2015-12-15T17:32:38	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.149%
2022-03-03T20:38:37	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.624%
2022-03-22T11:10:11	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.666%
2022-05-25T14:13:24	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.380%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-04T08:01:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-27T11:29:00	markr	Manual testing	2¹	2⁶²		-	-	0.164	-	-
2012-05-10T01:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.425	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.261	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.523	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.995	-	-
2016-02-28T22:17:30	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.990	-	-
2016-11-08T02:48:16	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.981	-	-
2019-02-04T14:28:11	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.962	-	-
2020-12-07T17:57:15	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	15.92	-	-
2021-03-24T08:51:07	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	31.85	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.356 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	3.356 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.837	43.321%
25	50000	0.077	92.559%
30	250000	0.005	99.512%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.794
50000	6700000	41968023079268567115719	2	0.346
50000	6750000		7	1.216

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-13T06:03:00	Sid & Andy	Slinky	50000	5000000						3	0.448
2012-06-02T11:47:00	Kamil_Górski	drugi	50000	5000000						3	0.448
2015-12-15T17:50:04	S36049	Wolle5	50000	5000000						3	0.448
2017-07-13T15:01:19	Bruce	Desk10	50000	5000000						3	0.448
2021-08-16T08:03:57	kutens	spica	50000	6750000						7	1.216
2021-10-30T00:05:14	kutens	spica	50000	6700000	41968023079268567115719	75.152	2	2	1259341485922657	2	0.346

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	Phantomas	v4_computers	075CEFE16F1F5E__	0.394

date

userid

compid

res64

spent (GHz-days)

1999-08-22T00:00:00

Phantomas

v4_computers

075CEFE16F1F5E__

0.394

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 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 110000, B2 = 2035000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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