M2198747 Mersenne number exponent details

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is 2 ^2198747 - 1

has 661889 decimal digits

takes 0.145 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	9A97D12509BE731A	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	2⁶⁸	27.1086	67.6471%	2500000	125000000	0.8746	7.9346%	27.9832	70.2141%	2.5671%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8628%	0.0193	63.1548%	1.0859%
GPU72	2⁶²	0.2794	64.5161%	11000	170000	0.0019	1.5998%	0.2813	65.0838%	0.5677%
Difference	+6	+26.8292	+3.1309%	+2489000	+124830000	+0.8728	+6.3348%	+27.7019	+5.1303%	+5.1303%

Known prime factors (1 factor, 80.6 bits, 0.00366692% 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
2198747	1866021736261269420045167	25	80.626	424337528660930389 29 × 1723 × 55381 × 153344207	2020-05-10	55381	153344207	145,813	0.8015	1.4877

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-05T01:17:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.199%
2010-11-09T10:51:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.355%
2011-01-10T19:10:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.207%
2014-07-04T02:21:00	Jocelyn Larouche	Manual testing	119191	119191		-		-	-	0.011	-	-	0.890%
2014-10-13T22:29:00	Jocelyn Larouche	Manual testing	148382	148382		-		-	-	0.014	-	-	1.007%
2016-02-05T12:25:21	Jocelyn Larouche	Manual testing	583200	5832000	6	-		-	-	0.083	-	-	3.939%
2018-03-27T19:29:55	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.935%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-03T02:27:00	Sturle Sunde	gibsy.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T00:01:00	Sturle Sunde	gnom.ifi	2⁶¹	2⁶²		-	-	0.140	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.446	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.893	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.699	-	-
2016-01-07T16:51:52	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.399	-	-
2016-12-03T03:08:56	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.797	-	-
2019-04-01T13:34:48	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.59	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.420 GHz-days
Estimated T-Level:	3.750

Digits	B1	Curves	Complete	FacMiss
20	11000	75 / 100	0.750	47.059%
25	50000	75 / 280	0.268	76.465%

New Calculation Method

Total ECM effort:	6.420 GHz-days
Estimated T-Level:	3.750

Digits	B1	Complete	FacMiss
20	11000	2.419	8.898%
25	50000	0.219	80.360%
30	250000	0.013	98.663%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		72	6.163
50000	5000000	1866021736261269420045167	3	0.257

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	9A97D12509BE731A	0.145
2018-04-15T21:16:57	kkmrkkblmbrbk	old	9A97D12509BE731A	0.145

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-05-11T07:46:56

Christoph Zenger

Manual testing

1866021736261269420045167

9AA740A6F56953A1

no

2020-05-13T06:10:49

ANONYMOUS

obFIV_MkQmyMzMWzFMY2

1866021736261269420045167

9AA740A6F56953A1

no

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 583200, B2 = 5832000 (P-1 stage 2)

B1 = 583200 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148382 (P-1 stage 1)

B1 = 119191 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-05-13T06:10:49+00:00