M3712927 Mersenne number exponent details

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M3712927

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is 2 ^3712927 - 1

has 1117703 decimal digits

takes 0.390 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	B4838FFEC05C2508	double-checked
PRP	37A0BB5EE95CD819	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	64.3564	68.5714%	14000000	700000000	7.8239	10.2453%	72.1803	71.7914%	3.2200%
PrimeNet	2⁶⁰	0.0414	63.3333%	16000	320000	0.0050	3.0855%	0.0463	64.4647%	1.1314%
GPU72	2⁶⁴	0.9586	65.6250%	22000	450000	0.0069	2.1069%	0.9655	66.3493%	0.7243%
Difference	+6	+63.3978	+2.9464%	+13978000	+699550000	+7.8170	+8.1384%	+71.2148	+5.4421%	+5.4421%

Known prime factors (1 factor, 95.4 bits, 0.00256842% 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
3712927	50973075838530719783420830513	29	95.364	6864271212244506797928 2³ × 3 × 286011300510187783247	2021-10-07	8	286011300510187783247	3.727e+9	2.373e+12	4.432e+12

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:47:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.729%
2012-12-09T07:51:00	Squeeky_Squirrel	T7500_2200	245000	7717500		-		-	-	0.099	-	-	3.247%
2021-05-14T15:49:28	axn	Manual testing	14000000	700000000		-		-	-	7.824	-	-	10.245%
2022-03-04T04:18:03	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.623%
2022-03-22T17:36:43	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.665%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-07T17:50:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-18T13:04:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.083	-	-
2012-04-19T23:27:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.430	-	-
2016-02-23T16:29:37	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.264	-	-
2015-01-20T20:48:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.529	-	-
2015-01-20T20:48:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.006	-	-
2016-02-23T16:35:12	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.013	-	-
2016-10-31T13:33:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.025	-	-
2019-02-04T14:28:13	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.051	-	-
2020-12-14T01:48:38	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.10	-	-
2021-03-06T17:44:05	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.20	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.897 GHz-days
Estimated T-Level:	1.250

Digits	B1	Curves	Complete	FacMiss
20	11000	25 / 100	0.250	77.782%
25	50000	25 / 280	0.089	91.444%

New Calculation Method

Total ECM effort:	3.897 GHz-days
Estimated T-Level:	1.250

Digits	B1	Complete	FacMiss
20	11000	0.822	43.954%
25	50000	0.075	92.809%
30	250000	0.005	99.541%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.790
50000	5000000	50973075838530719783420830513	6	0.895
50000	6750000		7	1.213

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-01T22:05:00	Marzbug	Xeon	50000	5000000						3	0.447
2012-05-17T07:28:00	Lukasz Wrobel	i-5	50000	5000000						3	0.447
2015-11-12T13:06:26	FreeTibet	DR	50000	5000000						3	0.447
2017-06-15T04:33:45	bayanne	iMac	50000	5000000						3	0.447
2021-07-29T09:18:23	kutens	terra	50000	6750000						7	1.213
2021-10-07T05:07:01	mnd9	50871b	50000	5000000	50973075838530719783420830513	95.364	6	2	5704346490608893	6	0.895

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-09T00:00:00	rpali	v4_computers	B4838FFEC05C2508	0.390
1998-01-05T00:00:00	rpali	v4_computers	B4838FFEC05C2508	0.390
1999-08-22T00:00:00	ANONYMOUS	v4_computers	B4838FFEC05C2508	0.390

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-13T17:36:04

RichD0

Linux-5

50973075838530719783420830513

37A0BB5EE95CD819

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 = 14000000, B2 = 700000000 (P-1 stage 2)

B1 = 14000000 (P-1 stage 1)

B1 = 245000, B2 = 7717500 (P-1 stage 2)

B1 = 245000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

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TF factor-bounds graph:

2⁷⁰

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Last modified: 2022-03-22T17:36:43+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