M3233651 Mersenne number exponent details

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M3233651

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>>>

is 2 ^3233651 - 1

has 973426 decimal digits

takes 0.275 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	8461DFAC73A1DDA4	double-checked
PRP	C4405B378F02D961	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	36.9201	68.1159%	3000000	90000000	0.9552	7.3252%	37.8753	70.4515%	2.3356%
PrimeNet	2⁶⁰	0.0475	63.3333%	14000	260000	0.0034	2.7684%	0.0509	64.3484%	1.0151%
GPU72	2⁶⁴	1.1007	65.6250%	16000	280000	0.0037	1.6532%	1.1045	66.1933%	0.5683%
Difference	+5	+35.8194	+2.4909%	+2984000	+89720000	+0.9515	+5.6720%	+36.7709	+4.2582%	+4.2582%

Known prime factors (1 factor, 77.1 bits, 0.00238538% 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
3233651	165908699799329601033041	24	77.135	25653464118318520 2³ × 5 × 11 × 17 × 31 × 110632500079	2021-08-12	31	110632500079	18,030	743.87	1,389.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:37:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.003	-	-	0.669%
2011-09-08T00:50:00	harlee	P4_2600	60000	1035000		-		-	-	0.014	-	-	1.688%
2014-06-11T02:09:00	Jocelyn Larouche	Manual testing	79849	79849		-		-	-	0.010	-	-	0.651%
2014-09-29T22:05:00	Jocelyn Larouche	Manual testing	99698	99698		-		-	-	0.012	-	-	0.747%
2016-01-12T16:09:37	Squeeky_Squirrel	P4_2600	165000	4455000	6	-		-	-	0.049	-	-	2.955%
2016-07-10T03:01:15	Jocelyn Larouche	Manual testing	375705	8910000	6	-		-	-	0.104	-	-	3.887%
2020-01-19T13:48:47	BigBrother	Winston	3000000	90000000	12	-		-	-	0.955	-	-	7.325%
2022-03-12T12:05:02	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.006%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-04T21:27:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-21T01:20:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.095	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.304	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.607	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.155	-	-
2015-06-24T21:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.311	-	-
2017-03-26T03:14:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.622	-	-
2018-11-26T14:19:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.244	-	-
2021-02-02T07:19:10	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.49	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.339 GHz-days
Estimated T-Level:	3.300

Digits	B1	Curves	Complete	FacMiss
20	11000	66 / 100	0.660	51.514%
25	50000	66 / 280	0.236	78.967%

New Calculation Method

Total ECM effort:	8.339 GHz-days
Estimated T-Level:	3.300

Digits	B1	Complete	FacMiss
20	11000	2.202	11.062%
25	50000	0.200	81.861%
30	250000	0.012	98.772%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	2.589
50000	5000000	165908699799329601033041	13	1.530
50000	6750000		28	3.810
50000	6800000		3	0.410

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-31T18:54:00	Smurgs	Praca	50000	5000000						3	0.353
2011-09-11T06:04:00	S00030	op9020-usff	50000	5000000						3	0.353
2014-05-27T04:03:00	Pool Party	St.P.p	50000	5000000						3	0.353
2016-08-15T09:34:49	f0rteOC	Fortissimo	50000	5000000						3	0.353
2018-10-27T01:16:49	volki	home	50000	5000000						3	0.353
2020-12-27T07:21:56	Zenzoma	AMD3970X	50000	5000000						7	0.824
2021-01-01T01:57:37	axn	Manual testing	50000	6800000						3	0.410
2021-02-17T16:19:13	Joe S.	6700k	50000	6750000						7	0.953
2021-02-17T20:41:59	Joe S.	Manual testing	50000	6750000						7	0.953
2021-02-17T20:42:16	Joe S.	Manual testing	50000	6750000						7	0.953
2021-02-17T20:42:28	Joe S.	Manual testing	50000	6750000						7	0.953
2021-08-12T11:24:06	MarkS	laptop64	50000	5000000	165908699799329601033041	77.135	13	2	4228228985849494	13	1.530

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-16T00:00:00	ANONYMOUS	v4_computers	8461DFAC73A1DDA4	0.275
1998-06-28T00:00:00	ANONYMOUS	v4_computers	8461DFAC73A1DDA4	0.275
1999-06-15T00:00:00	ANONYMOUS	v4_computers	8461DFAC73A1DDA4	0.275

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-12T22:25:37

GURA LOVE

165908699799329601033041

C4405B378F02D961

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 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 375705, B2 = 8910000 (P-1 stage 2)

B1 = 165000, B2 = 4455000 (P-1 stage 2)

B1 = 375705 (P-1 stage 1)

B1 = 165000 (P-1 stage 1)

B1 = 60000, B2 = 1035000 (P-1 stage 2)

B1 = 99698 (P-1 stage 1)

B1 = 79849 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-12T12:05:02+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