M1187047 Mersenne number exponent details

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M1187047

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is 2 ^1187047 - 1

has 357337 decimal digits

takes 0.036 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	824457244418F62A	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	25.0318	68.6567%	300000	10000000	0.0368	4.1554%	25.0686	69.9592%	1.3024%
PrimeNet	2⁵⁶	0.0081	62.5000%	5000	80000	0.0004	2.2649%	0.0085	63.3494%	0.8494%
GPU72	2⁶⁰	0.1294	65.0000%	5000	28000	0.0003	0.8009%	0.1297	65.2803%	0.2803%
Difference	+7	+24.9024	+3.6567%	+295000	+9972000	+0.0366	+3.3546%	+24.9390	+4.6789%	+4.6789%

Known prime factors (2 factors, 157.1 bits, 0.01323424% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1187047	39292462221892505897	20	65.091	16550508203084 2² × 4137627050771	2007-10-17	4	4137627050771	11.929	10,024	18,722
1187047	4971377754667092662022322679	28	92.006	2094010496074330949837 79 × 131 × 120929 × 292849 × 5713553	2014-12-24	292849	5713553	1.188e+9	0.0262	0.0265

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1187047	39292462221892505897 4971377754667092662022322679	195337672616013528816673434795979360995644338063	48	157.097

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.005%
2002-08-31T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	8.89333e-5	-	-	0.018%
2002-08-31T00:00:00	Jocelyn Larouche	v4_computers	3000	3000		-		-	-	0.000	-	-	0.034%
2002-08-31T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.049%
2002-09-14T00:00:00	Jocelyn Larouche	v4_computers	5000	5000		-		-	-	0.000	-	-	0.065%
2002-09-22T00:00:00	Jocelyn Larouche	v4_computers	8000	8000		-		-	-	0.000	-	-	0.111%
2002-09-29T00:00:00	Jocelyn Larouche	v4_computers	10000	10000		-		-	-	0.000	-	-	0.139%
2003-09-21T00:00:00	ANONYMOUS	v4_computers	10000	1000000		-		-	-	0.003	-	-	0.990%
2014-12-24T12:03:00	alpertron	Manual testing	300000	10000000	12		4971377754667092662022322679	28	92.006	0.037	0.073	0.074	4.155%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.032	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.259	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.259	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.827	-	-
2022-04-12T20:41:58	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.654	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.445 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.445 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		39292462221892505897	1	0.00000e+0
50000	5000000		281	10.35
250000	25000000		44	8.099

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-17T18:13:00	James Heinrich	WHS			39292462221892505897	65.091		1		1	-
2017-09-01T10:41:45	TJAOI	Manual testing	50000	5000000						140	5.154
2018-05-25T15:39:22	TJAOI	Manual testing	50000	5000000						141	5.191
2021-02-12T10:29:52	TJAOI	Manual testing	250000	25000000						44	8.099

Lucas-Lehmer results:
No L-L results for M1187047

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T11:20:44

Oliver Kruse

GTX-1

39292462221892505897

4971377754667092662022322679

D01705104344AD8F

2017-10-05T21:15:39

Oliver Kruse

Manual testing

39292462221892505897

4971377754667092662022322679

D01705104344AD__

2017-10-17T17:53:26

Oliver Kruse

Threadripper

39292462221892505897

4971377754667092662022322679

D01705104344AD__

2018-01-03T01:45:18

ATH

ec2-8x

39292462221892505897

4971377754667092662022322679

D01705104344AD__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 10000, B2 = 1000000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 8000 (P-1 stage 1)

B1 = 5000 (P-1 stage 1)

B1 = 4000 (P-1 stage 1)

B1 = 3000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

B1 = 1000 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-12T20:41:58+00:00

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