M3743863 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	Prob over default TF
Actual	2⁶⁷	7.9367	67.1642%	100000	130364850	1.0961	6.0076%	9.0328	69.1368%	1.9727%
PrimeNet	2⁶⁰	0.0410	63.3333%	16000	320000	0.0050	3.0900%	0.0460	64.4663%	1.1330%
GPU72	2⁶⁴	0.9507	65.6250%	22000	450000	0.0069	2.1101%	0.9576	66.3503%	0.7253%
Difference	+3	+6.9860	+1.5392%	+78000	+129914850	+1.0892	+3.8976%	+8.0752	+2.7865%	+2.7865%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.9367

67.1642%

100000

130364850

1.0961

6.0076%

9.0328

69.1368%

1.9727%

PrimeNet

2⁶⁰

0.0410

63.3333%

16000

320000

0.0050

3.0900%

0.0460

64.4663%

1.1330%

GPU72

2⁶⁴

0.9507

65.6250%

22000

450000

0.0069

2.1101%

0.9576

66.3503%

0.7253%

Difference

+6.9860

+1.5392%

+78000

+129914850

+1.0892

+3.8976%

+8.0752

+2.7865%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3743863	7727333233	10	32.847	1032 2³ × 3 × 43	-	8	43	1.870e-10	1.509e-6	2.479e-6
3743863	32204709527	11	34.907	4301 11 × 17 × 23	2008-09-07	17	23	1.180e-9	2.639e-6	5.269e-6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3743863

7727333233

32.847

1032
2³ × 3 × 43

1.870e-10

1.509e-6

2.479e-6

3743863

32204709527

34.907

4301
11 × 17 × 23

2008-09-07

1.180e-9

2.639e-6

5.269e-6

exponent	prime factors	composite factor	digits	bits*
3743863	7727333233 32204709527	248856522187098810791	21	67.754

exponent

prime factors

composite factor

digits

bits*

3743863

7727333233
32204709527

248856522187098810791

67.754

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-03-04T19:33:09	Jocelyn Larouche	Manual testing	90000	90000		-	skipped known factor: 7727333233 skipped known factor: 32204709527	-	-	0.014	-	-	0.961%
2022-03-22T11:08:52	Jocelyn Larouche	Manual testing	100000	100000		-	skipped known factor: 7727333233 skipped known factor: 32204709527	-	-	0.015	-	-	1.021%
2022-05-23T20:33:48	Jocelyn Larouche	Manual testing	100000	130364850		-	skipped known factor: 7727333233 skipped known factor: 32204709527	-	-	1.096	-	-	6.008%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07T21:11:00	Will Edgington	Manual testing	?	?	32204709527	34.907	11	5.69103e-10	0.840	1.21589e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.448 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.448 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.448

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-14T18:19:45	rucio		50000	5000000						3	0.448

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:17:47

kkmrkkblmbrbk

Manual testing

7727333233

32204709527

AE786EBC1028D0__

2017-12-03T23:31:17

Oliver Kruse

GTX-0

7727333233

32204709527

AE786EBC1028D0__

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 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

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