M1656947 Mersenne number exponent details

Residue

Status

L-L

B90CACD7432A47B7

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	17.9329	68.6567%	500000	15000000	0.0880	5.0082%	18.0210	70.2265%	1.5697%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5655%	0.0125	64.1031%	0.9452%
GPU72	2⁶¹	0.1854	65.5738%	7000	70000	0.0007	1.1521%	0.1861	65.9704%	0.3966%
Difference	+6	+17.7475	+3.0829%	+493000	+14930000	+0.0873	+3.8561%	+17.8349	+4.2560%	+4.2560%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.9329

68.6567%

500000

15000000

0.0880

5.0082%

18.0210

70.2265%

1.5697%

PrimeNet

2⁵⁷

0.0116

63.1579%

7000

120000

0.0009

2.5655%

0.0125

64.1031%

0.9452%

GPU72

2⁶¹

0.1854

65.5738%

7000

70000

0.0007

1.1521%

0.1861

65.9704%

0.3966%

Difference

+17.7475

+3.0829%

+493000

+14930000

+0.0873

+3.8561%

+17.8349

+4.2560%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1656947	6266477663043915817	19	62.442	1890971063964 2² × 3³ × 17508991333	2016-08-10	27	17508991333	0.4277	65.097	121.58
1656947	88220682361522473767	20	66.258	26621455713889 26621455713889	2010-05-18	1	26621455713889	13.343	98,977	184,861

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1656947

6266477663043915817

62.442

1890971063964
2² × 3³ × 17508991333

2016-08-10

17508991333

0.4277

65.097

121.58

1656947

88220682361522473767

66.258

26621455713889
26621455713889

2010-05-18

26621455713889

13.343

98,977

184,861

exponent	prime factors	composite factor	digits	bits*
1656947	6266477663043915817 88220682361522473767	552832935436972955875612715320338872639	39	128.700

exponent

prime factors

composite factor

digits

bits*

1656947

6266477663043915817
88220682361522473767

552832935436972955875612715320338872639

128.700

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:00	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.008%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-05-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2022-03-08T23:06:21	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2022-03-09T02:40:38	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.093	-	-
2010-04-27T22:40:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.093	-	-
2022-03-08T23:06:21	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.185	-	-
2016-08-10T15:14:01	TJAOI	Manual testing	2⁶²	2⁶³*	6266477663043915817	62.442	19	0.057	0.158	0.116

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.821 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	14.821 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.065	0.031%
25	50000	0.729	48.246%
30	250000	0.045	95.611%
35	1000000	0.002	99.795%

ECM Summary

B1	B2	factor	curves	GHz-days
		88220682361522473767	1	0.00000e+0
50000	5000000		250	14.82

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-22T21:06:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-10T05:16:00	James Hintz	20_060209	50000	5000000						3	0.178
2010-05-18T20:46:00	Chang Chia-Tche	sekhmet			88220682361522473767	66.258		1		1	-
2019-12-16T13:26:49	TJAOI	Manual testing	50000	5000000						244	14.46

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	B90CACD7432A47B7	0.078

date

userid

compid

res64

spent (GHz-days)

1998-12-06T00:00:00

ANONYMOUS

v4_computers

B90CACD7432A47B7

0.078

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T19:59:59

Oliver Kruse

GTX-0

6266477663043915817

88220682361522473767

5C2A65EA425F5481

2017-10-03T00:12:06

kkmrkkblmbrbk

Manual testing

6266477663043915817

88220682361522473767

5C2A65EA425F54__

2017-11-14T00:56:06

ATH

ec2-1xf

6266477663043915817

88220682361522473767

5C2A65EA425F54__

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 = 15000000 (P-1 stage 2)

B1 = 500000 (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

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