M3233653 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	2⁶⁸	18.4327	67.6471%	1000000	134343300	1.0200	7.6388%	19.4527	70.1184%	2.4714%
PrimeNet	2⁶⁰	0.0475	63.3333%	14000	260000	0.0034	2.7684%	0.0509	64.3484%	1.0151%
GPU72	2⁶⁴	1.1007	65.6250%	16000	280000	0.0037	1.6532%	1.1045	66.1933%	0.5683%
Difference	+4	+17.3320	+2.0221%	+984000	+134063300	+1.0162	+5.9855%	+18.3482	+3.9251%	+3.9251%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.4327

67.6471%

1000000

134343300

1.0200

7.6388%

19.4527

70.1184%

2.4714%

PrimeNet

2⁶⁰

0.0475

63.3333%

14000

260000

0.0034

2.7684%

0.0509

64.3484%

1.0151%

GPU72

2⁶⁴

1.1007

65.6250%

16000

280000

0.0037

1.6532%

1.1045

66.1933%

0.5683%

Difference

+17.3320

+2.0221%

+984000

+134063300

+1.0162

+5.9855%

+18.3482

+3.9251%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3233653	12721190903	11	33.567	1967 7 × 281	-	7	281	5.046e-10	2.706e-6	3.523e-6
3233653	14362541426353	14	43.707	2220792 2³ × 3 × 7 × 13219	2008-09-30	8	13219	6.127e-7	8.982e-5	0.0002

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3233653

12721190903

33.567

1967
7 × 281

281

5.046e-10

2.706e-6

3.523e-6

3233653

14362541426353

43.707

2220792
2³ × 3 × 7 × 13219

2008-09-30

13219

6.127e-7

8.982e-5

0.0002

exponent	prime factors	composite factor	digits	bits*
3233653	12721190903 14362541426353	182708631336882428066759	24	77.274

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-16T04:02:56	Jocelyn Larouche	Manual testing	323365	3233653	6	-	skipped known factor: 12721190903 skipped known factor: 14362541426353	-	-	0.059	-	-	3.383%
2022-03-09T23:05:30	Jocelyn Larouche	Manual testing	1000000	134343300		-	skipped known factor: 12721190903 skipped known factor: 14362541426353	-	-	1.020	-	-	7.639%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:46:00	markr	Manual testing	?	?	14362541426353	43.707	14	2.50369e-7	0.606	5.51413e-7
2021-10-01T11:11:55	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.244	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.353 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:	0.353 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	0.353

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-09-14T08:28:34	ATH	ec2-ECMCF	50000	5000000						3	0.353

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-02T07:39:31

Oliver Kruse

GTX-2

12721190903

14362541426353

AEDBCD37E9C6DF__

2017-12-13T14:55:03

kkmrkkblmbrbk

c4.xlarge

12721190903

14362541426353

AEDBCD37E9C6DF__

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 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 323365, B2 = 3233653 (P-1 stage 2)

B1 = 323365 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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