M3979201 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	14.9791	67.6471%	500000	113097600	1.1999	7.0121%	16.1790	69.9157%	2.2686%
PrimeNet	2⁶¹	0.0772	63.9344%	16000	320000	0.0059	2.7254%	0.0831	64.9174%	0.9829%
GPU72	2⁶⁵	1.8335	66.1538%	20000	360000	0.0070	1.7018%	1.8404	66.7298%	0.5760%
Difference	+3	+13.1456	+1.4932%	+480000	+112737600	+1.1929	+5.3103%	+14.3385	+3.1859%	+3.1859%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

14.9791

67.6471%

500000

113097600

1.1999

7.0121%

16.1790

69.9157%

2.2686%

PrimeNet

2⁶¹

0.0772

63.9344%

16000

320000

0.0059

2.7254%

0.0831

64.9174%

0.9829%

GPU72

2⁶⁵

1.8335

66.1538%

20000

360000

0.0070

1.7018%

1.8404

66.7298%

0.5760%

Difference

+13.1456

+1.4932%

+480000

+112737600

+1.1929

+5.3103%

+14.3385

+3.1859%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3979201	110780955841	12	36.689	13920 2⁵ × 3 × 5 × 29	-	32	32	2.331e-9	5.787e-6	1.178e-5
3979201	2340033859247773681249	22	70.987	294033131179824 2⁴ × 3 × 6125690232913	2018-11-26	16	6125690232913	84.556	60,357	112,730

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3979201

110780955841

36.689

13920
2⁵ × 3 × 5 × 29

2.331e-9

5.787e-6

1.178e-5

3979201

2340033859247773681249

70.987

294033131179824
2⁴ × 3 × 6125690232913

2018-11-26

6125690232913

84.556

60,357

112,730

exponent	prime factors	composite factor	digits	bits*
3979201	110780955841 2340033859247773681249	259231187627772425660007478725409	33	107.676

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-19T17:52:32	Jocelyn Larouche	Manual testing	300000	300000		-	skipped known factor: 110780955841	-	-	0.054	-	-	1.589%
2022-05-11T11:03:50	Jocelyn Larouche	Manual testing	500000	113097600		-	skipped known factor: 110780955841	-	-	1.200	-	-	7.012%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-02-25T17:23:57	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	7.512	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.539 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:	0.539 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	2340033859247773681249	3	0.539

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-26T07:04:48	MarkS	laptop64	50000	5000000	2340033859247773681249	70.987	3	2		3	0.539

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:12:51

kkmrkkblmbrbk

Manual testing

110780955841

E4D29D94725223__

2018-01-03T08:36:26

Oliver Kruse

GTX-1

110780955841

E4D29D94725223__

2018-11-28T22:36:11

Oliver Kruse

GTX-0

110780955841

2340033859247773681249

38D744F70FF9CF__

2018-11-29T11:38:58

kkmrkkblmbrbk

c5d.large

110780955841

2340033859247773681249

38D744F70FF9CF__

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 = 500000, B2 = 113097600 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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