M888637 Mersenne number exponent details

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M888637

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is 2 ⁸⁸⁸⁶³⁷ - 1

has 267507 decimal digits

takes 0.022 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	E6174AA9133C52__	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	33.4376	70.1493%	300000	10000000	0.0291	4.0027%	33.4668	71.3441%	1.1948%
PrimeNet	2⁴⁰	0.0000	50.0000%	8000	340000	0.0009	23.1182%	0.0009	61.5591%	11.5591%
GPU72	2⁴⁴	0.0000	54.5455%	15000	600000	0.0016	17.9621%	0.0017	62.7100%	8.1646%
Difference	+23	+33.4376	+15.6038%	+285000	+9400000	+0.0275	-13.9595%	+33.4651	+8.6340%	+8.6340%

Known prime factors (1 factor, 74.0 bits, 0.00833140% 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
888637	19365379689397248683977	23	74.036	10896113761523124 2² × 3 × 1929589 × 470571443	2007-09-07	1929589	470571443	8,018.1	0.9656	1.6837

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.210%
2002-02-17T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.446%
2002-04-20T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.802%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.300%
2002-07-14T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.945%
2002-12-25T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.015	-	-	2.731%
2003-08-25T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.644%
2016-03-17T18:52:59	alpertron	Manual testing	300000	10000000	12	-		-	-	0.029	-	-	4.003%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.011	-	-
2001-12-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.022	-	-
2003-08-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.043	-	-
2022-03-07T09:56:28	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.043	-	-
2004-08-20T00:00:00	Sturle Sunde	v4_computers	2¹	2⁶⁰		-	-	0.173	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.052 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:	14.052 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
		19365379689397248683977	1	0.00000e+0
50000	5000000		281	7.882
250000	25000000		44	6.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-07T12:08:00	Team_Bundu	bundu1			19365379689397248683977	74.036		1		1	-
2016-02-12T13:35:07	TJAOI	Manual testing	50000	5000000						100	2.805
2016-12-16T18:18:59	TJAOI	Manual testing	50000	5000000						90	2.524
2017-08-11T11:13:28	TJAOI	Manual testing	50000	5000000						91	2.552
2019-12-02T14:35:24	TJAOI	Manual testing	250000	25000000						44	6.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-01-28T00:00:00	ANONYMOUS	v4_computers	E6174AA9133C52__	0.022

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T07:03:04

Oliver Kruse

GTX-1

19365379689397248683977

1727BF9A05C0A8__

2017-10-14T14:57:01

Oliver Kruse

Threadripper

1727BF9A05C0A8__

2017-12-19T13:25:16

ATH

ec2-1xf

19365379689397248683977

1727BF9A05C0A8__

2020-04-22T19:05:26

Oliver Kruse

AddPrpType5

19365379689397248683977

F210D0D9798958__

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

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

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

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T09:56:28+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