M2648207 Mersenne number exponent details

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M2648207

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is 2 ^2648207 - 1

has 797190 decimal digits

takes 0.205 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	3620F98D92F7D759	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	22.5076	67.6471%	2000000	50000000	0.5169	6.8574%	23.0245	69.8656%	2.2186%
PrimeNet	2⁵⁹	0.0290	62.7119%	11000	200000	0.0024	2.7040%	0.0314	63.7201%	1.0083%
GPU72	2⁶³	0.6027	65.0794%	13000	200000	0.0026	1.5745%	0.6053	65.6292%	0.5498%
Difference	+5	+21.9050	+2.5677%	+1987000	+49800000	+0.5143	+5.2829%	+22.4192	+4.2364%	+4.2364%

Known prime factors (1 factor, 74.3 bits, 0.00280729% 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
2648207	23958903292561292392177	23	74.343	4523608481618184 2³ × 3 × 7 × 83 × 281 × 1154493031	2020-07-14	281	1154493031	1,865.0	7.0443	13.157

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.239%
2009-06-22T14:24:00	harlee	P4_2600	30000	420000		-		-	-	0.006	-	-	1.207%
2011-01-17T07:25:00	James Heinrich	i7-920	180000	4275000		-		-	-	0.045	-	-	3.228%
2016-12-28T03:20:12	Jocelyn Larouche	low 4M	171988	171988		-		-	-	0.019	-	-	1.126%
2016-12-29T21:56:29	Jocelyn Larouche	low 4M	206385	206385		-		-	-	0.023	-	-	1.238%
2017-05-08T05:55:49	Jocelyn Larouche	low 4M	360000	3600000	6	-		-	-	0.060	-	-	3.423%
2019-11-29T02:54:12	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.857%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	Ethan O'Connor	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:18	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-30T23:08:00	Sturle Sunde	golan.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-
2012-06-10T01:55:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.116	-	-
2013-01-23T08:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.371	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.741	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.411	-	-
2016-01-21T23:03:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.822	-	-
2017-09-08T08:21:16	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.644	-	-
2019-02-18T10:31:25	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.29	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.614 GHz-days
Estimated T-Level:	1.750

Digits	B1	Curves	Complete	FacMiss
20	11000	35 / 100	0.350	70.345%
25	50000	35 / 280	0.125	88.230%

New Calculation Method

Total ECM effort:	3.614 GHz-days
Estimated T-Level:	1.750

Digits	B1	Complete	FacMiss
20	11000	1.129	32.335%
25	50000	0.102	90.299%
30	250000	0.006	99.374%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	3.408
50000	5000000	23958903292561292392177	2	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-03T17:36:00	borkencode	CFF2DC1CD	50000	5000000						3	0.310
2010-07-16T17:08:00	lindee	amokram	50000	5000000						3	0.310
2012-11-30T08:26:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.310
2014-11-05T23:08:00	arnaud	srv-630	50000	5000000						3	0.310
2016-01-20T06:22:56	Jason U	Server7	50000	5000000						3	0.310
2016-04-10T04:20:07	Syntony	Geomancer	50000	5000000						3	0.310
2016-09-18T00:40:35	Ismo Laitela		50000	5000000						3	0.310
2017-06-30T21:50:02	Sebastian Hornbostel	V2	50000	5000000						3	0.310
2017-11-01T16:06:27	Sebastian Hornbostel	V2	50000	5000000						3	0.310
2018-05-09T21:12:02	Ducho_YYZ	Dutch	50000	5000000						3	0.310
2019-05-17T22:36:22	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2020-07-14T16:31:28	MarkS	desktop-i7	50000	5000000	23958903292561292392177	74.343	2	2	8216092358910113	2	0.207

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	Ethan O'Connor	v4_computers	3620F98D92F7D759	0.205
2018-07-16T17:29:07	kkmrkkblmbrbk	old	3620F98D92F7D759	0.205

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-15T01:31:35

pew

10980xe_1

23958903292561292392177

FBB928DBE4581003

2020-07-15T03:07:51

oodaira

com2

23958903292561292392177

FBB928DBE4581003

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 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 360000, B2 = 3600000 (P-1 stage 2)

B1 = 180000, B2 = 4275000 (P-1 stage 2)

B1 = 360000 (P-1 stage 1)

B1 = 206385 (P-1 stage 1)

B1 = 180000 (P-1 stage 1)

B1 = 171988 (P-1 stage 1)

B1 = 30000, B2 = 420000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-15T03:07:51+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