M3669691 Mersenne number exponent details

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M3669691

<<<

>>>

is 2 ^3669691 - 1

has 1104688 decimal digits

takes 0.385 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	3CA790F5B4C46827	double-checked
PRP	A1C366CEFB293E36	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	2⁷⁰	65.1146	68.5714%	30000000	600000000	9.2981	10.3792%	74.4128	71.8335%	3.2620%
PrimeNet	2⁶⁰	0.0419	63.3333%	16000	320000	0.0050	3.0793%	0.0468	64.4624%	1.1291%
GPU72	2⁶⁴	0.9699	65.6250%	22000	400000	0.0065	2.0382%	0.9764	66.3256%	0.7006%
Difference	+6	+64.1447	+2.9464%	+29978000	+599600000	+9.2916	+8.3410%	+73.4363	+5.5078%	+5.5078%

Known prime factors (1 factor, 73.4 bits, 0.00199945% 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
3669691	12237733910340310241057	23	73.374	1667406589593008 2⁴ × 11 × 9473901077233	2021-07-01	16	9473901077233	1,002.8	78,607	146,816

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-11T19:29:00	Carsten Kossendey	durandal	20000	260000		-		-	-	0.005	-	-	0.722%
2012-02-07T15:34:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	1.878%
2016-06-24T05:29:27	Jocelyn Larouche	Manual testing	90000	3285000	6	-		-	-	0.040	-	-	2.214%
2016-10-03T01:22:55	Jocelyn Larouche	low 4M	90000	3942000		-		-	-	0.046	-	-	2.305%
2016-12-24T20:28:42	Jocelyn Larouche	low 4M	108000	108000		-		-	-	0.016	-	-	0.695%
2016-12-30T22:58:50	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.776%
2017-01-30T01:30:57	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	0.898%
2017-02-13T00:36:34	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.479%
2020-10-14T01:56:54	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.379%
2022-03-04T04:18:54	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.621%
2022-03-22T11:10:31	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.663%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-08T06:42:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-06-06T05:22:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.084	-	-
2012-06-05T02:31:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.435	-	-
2016-02-23T16:29:36	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.268	-	-
2015-01-23T13:18:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.535	-	-
2015-01-23T13:18:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.018	-	-
2015-10-20T08:54:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.036	-	-
2017-01-03T07:36:03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.073	-	-
2018-11-12T14:47:29	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.145	-	-
2020-11-11T17:44:58	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.29	-	-
2021-02-25T02:26:50	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.58	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.827 GHz-days
Estimated T-Level:	0.950

Digits	B1	Curves	Complete	FacMiss
20	11000	19 / 100	0.190	82.617%
25	50000	19 / 280	0.068	93.428%

New Calculation Method

Total ECM effort:	2.827 GHz-days
Estimated T-Level:	0.950

Digits	B1	Complete	FacMiss
20	11000	0.613	54.178%
25	50000	0.055	94.611%
30	250000	0.003	99.659%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.786
50000	5000000	12237733910340310241057	7	1.042

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-23T06:05:00	LordJulius	Blackbox	50000	5000000						3	0.446
2012-06-22T17:45:00	oodaira	04	50000	5000000						3	0.446
2012-06-22T22:03:00	oodaira	Linux01	50000	5000000						3	0.446
2017-05-27T15:15:25	jafarism	jafarism-r07	50000	5000000						3	0.446
2021-07-01T21:15:26	daveward2005	Dave2	50000	5000000	12237733910340310241057	73.374	7	2	95363568725364	7	1.042

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-16T00:00:00	ANONYMOUS	v4_computers	3CA790F5B4C46827	0.385
1999-09-14T00:00:00	ANONYMOUS	v4_computers	3CA790F5B4C46827	0.385

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-07-03T02:42:46

Yizhe Huang

lap

12237733910340310241057

A1C366CEFB293E36

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 = 30000000, B2 = 600000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 241228, B2 = 2412280 (P-1 stage 2)

B1 = 90000, B2 = 3942000 (P-1 stage 2)

B1 = 90000, B2 = 3285000 (P-1 stage 2)

B1 = 241228 (P-1 stage 1)

B1 = 90000, B2 = 1642500 (P-1 stage 2)

B1 = 167520 (P-1 stage 1)

B1 = 129600 (P-1 stage 1)

B1 = 108000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-22T11:10:31+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