M332803 Mersenne number exponent details

Residue

Status

L-L

77728FE54121E3__

double-checked

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	89.2838	71.6418%	131072	13107200	0.0086	3.1703%	89.2924	72.5408%	0.8990%
PrimeNet	2⁴⁰	0.0000	52.5000%	3400	100000	0.0001	16.1623%	0.0001	60.1771%	7.6771%
GPU72	2⁴⁴	0.0000	56.8182%	6000	170000	0.0002	11.9591%	0.0002	61.9823%	5.1641%
Difference	+23	+89.2838	+14.8236%	+125072	+12937200	+0.0085	-8.7888%	+89.2923	+10.5585%	+10.5585%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

89.2838

71.6418%

131072

13107200

0.0086

3.1703%

89.2924

72.5408%

0.8990%

PrimeNet

2⁴⁰

0.0000

52.5000%

3400

100000

0.0001

16.1623%

0.0001

60.1771%

7.6771%

GPU72

2⁴⁴

0.0000

56.8182%

6000

170000

0.0002

11.9591%

0.0002

61.9823%

5.1641%

Difference

+23

+89.2838

+14.8236%

+125072

+12937200

+0.0085

-8.7888%

+89.2923

+10.5585%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
332803	240342434319678073057	21	67.704	361088142714576 2⁴ × 3² × 31 × 80888920859	2014-06-05	31	80888920859	105.15	45.442	84.872
332803	1298378461078588435749973321	28	90.069	1950671209512216590220 2² × 3 × 5 × 32511186825203609837	2007-08-14	5	32511186825203609837	812,138,100	1.826e+10	3.411e+10

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

332803

240342434319678073057

67.704

361088142714576
2⁴ × 3² × 31 × 80888920859

2014-06-05

80888920859

105.15

45.442

84.872

332803

1298378461078588435749973321

90.069

1950671209512216590220
2² × 3 × 5 × 32511186825203609837

2007-08-14

32511186825203609837

812,138,100

1.826e+10

3.411e+10

exponent	prime factors	composite factor	digits	bits*
332803	240342434319678073057 1298378461078588435749973321	312055440003865334468717428386318635896438912297	48	157.772

exponent

prime factors

composite factor

digits

bits*

332803

240342434319678073057
1298378461078588435749973321

312055440003865334468717428386318635896438912297

157.772

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-24T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.001	-	-	1.405%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.002	-	-	1.635%
2002-08-17T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.004	-	-	2.338%
2003-03-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.009	-	-	3.170%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	332803	332803		-		-	-	0.003	-	-	1.269%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.007	-	-
2022-03-07T06:36:37	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.007	-	-
2001-03-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.029	-	-
2002-03-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.058	-	-
2004-01-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.115	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.644 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	422 / 100	4.220	1.439%
25	50000	422 / 280	1.507	22.095%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	7.644 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.783	0.000%
25	50000	3.017	4.892%
30	250000	0.286	75.100%
35	1000000	0.022	97.835%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		240342434319678073057	1	0.00000e+0
		1298378461078588435749973321	1	0.00000e+0
50000	5000000		278	2.129
250000	25000000		144	5.515

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-14T15:47:00	Team_Bundu	bundu1			1298378461078588435749973321	90.069		1		1	-
2014-06-05T00:26:00	Richard B. Woods	Puttputt	50000	5000000						7	0.054
2014-06-05T00:26:00	Richard B. Woods	Puttputt			240342434319678073057	67.704		1		1	-
2014-10-10T12:41:00	TJAOI	Manual testing	50000	5000000						50	0.383
2015-02-20T13:27:00	TJAOI	Manual testing	50000	5000000						40	0.306
2015-12-04T11:27:57	TJAOI	Manual testing	50000	5000000						90	0.689
2016-05-20T14:52:27	TJAOI	Manual testing	50000	5000000						91	0.697
2018-01-19T13:23:09	TJAOI	Manual testing	250000	25000000						44	1.685
2019-09-02T12:28:35	TJAOI	Manual testing	250000	25000000						100	3.830

date	userid	compid	res64	spent (GHz-days)
2002-02-03T00:00:00	ANONYMOUS	v4_computers	77728FE54121E3__	0.002

date

userid

compid

res64

spent (GHz-days)

2002-02-03T00:00:00

ANONYMOUS

v4_computers

77728FE54121E3__

0.002

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T20:40:47

Oliver Kruse

Ollaptop

F094CA76066A27__

2017-09-23T17:10:55

Oliver Kruse

Manual testing

F094CA76066A27__

2017-10-13T02:43:02

Oliver Kruse

GTX-2

F094CA76066A27__

2017-12-12T14:30:01

ATH

xps

240342434319678073057

1298378461078588435749973321

F094CA76066A27__

2020-04-18T15:10:00

Oliver Kruse

AddPrpType5

240342434319678073057

1298378461078588435749973321

F4449C75F7E4BC__

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 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 332803 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (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

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

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