M3737131 Mersenne number exponent details

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M3737131

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>>>

is 2 ^3737131 - 1

has 1124989 decimal digits

takes 0.393 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	15.9494	67.6471%	1000000	1010447130	8.5279	10.0023%	24.4772	70.8831%	3.2360%
PrimeNet	2⁶⁰	0.0411	63.3333%	16000	320000	0.0050	3.0890%	0.0461	64.4660%	1.1326%
GPU72	2⁶⁴	0.9524	65.6250%	22000	450000	0.0069	2.1094%	0.9593	66.3501%	0.7251%
Difference	+4	+14.9969	+2.0221%	+978000	+1009997130	+8.5210	+7.8929%	+23.5179	+4.5330%	+4.5330%

Known prime factors (4 factors, 246.3 bits, 0.00658930% 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
3737131	161456346886729	15	47.198	21601644 2² × 3 × 1800137	-	4	1800137	8.431e-6	0.0149	0.0279
3737131	9734540416718881	16	53.112	1302408240 2⁴ × 3 × 5 × 7² × 110749	2014-09-04	49	110749	0.0005	0.0009	0.0017
3737131	1073241228883391718769	22	69.862	143591598593064 2³ × 3² × 1994327758237	2018-11-15	9	1994327758237	60.782	16,547	30,906
3737131	79756687312821920818433	23	76.078	10670844467697536 2⁷ × 1249 × 48187 × 1385149	2020-11-15	48187	1385149	7,069.9	0.0184	0.0215

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3737131	161456346886729 9734540416718881	1571703334304647124645542630249	31	100.310
3737131	161456346886729 1073241228883391718769	173281608143736208645643413466316601	36	117.061
3737131	9734540416718881 1073241228883391718769	10447510119454415965377457790084377489	38	122.974
3737131	161456346886729 79756687312821920818433	12877223373315353868256790651226275657	38	123.276
3737131	9734540416718881 79756687312821920818433	776394696150274990349916571548003933473	39	129.190
3737131	1073241228883391718769 79756687312821920818433	85598165103281415533089250559139551047268977	44	145.940
3737131	161456346886729 9734540416718881 1073241228883391718769	16868168179492437160476016601194463898023251604434 81	52	170.173
3737131	161456346886729 9734540416718881 79756687312821920818433	12535385138265535935971998296497945026436764958257 9817	54	176.388
3737131	161456346886729 1073241228883391718769 79756687312821920818433	13820367037782905305547858801397826875227777266171 814706233	59	193.139
3737131	9734540416718881 1073241228883391718769 79756687312821920818433	83325879779486864825615954218293729138493978262588 6201454737	60	199.053
3737131	161456346886729 9734540416718881 1073241228883391718769 79756687312821920818433	13453492150318709000724487327342601329448345818528 6139606771165940759485273	75	246.251

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-11-15T14:40:40	Jocelyn Larouche	Manual testing	373713	3737131	6		79756687312821920818433	23	76.078	0.085	0.785	0.170	3.629%
2022-01-18T07:18:59	Jocelyn Larouche	Manual testing	1000000	431367300		-	skipped known factor: 161456346886729 skipped known factor: 9734540416718881 skipped known factor: 79756687312821920818433	-	-	3.723	-	-	9.050%
2022-03-21T14:12:59	Jocelyn Larouche	Manual testing	1000000	1010447130		-	skipped known factor: 161456346886729 skipped known factor: 9734540416718881 skipped known factor: 79756687312821920818433	-	-	8.528	-	-	10.002%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-09-04T09:36:00	TJAOI	Manual testing	?	?	9734540416718881	53.112	16	0.000	0.838	0.000
2022-01-18T07:19:04	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	7.998	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.149 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.149 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1073241228883391718769	1	0.149

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-15T06:27:50	MarkS	laptop64	50000	5000000	1073241228883391718769	69.862	1	2		1	0.149

Lucas-Lehmer results:
No L-L results for M3737131

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-11T23:50:25

Oliver Kruse

GTX-0

161456346886729

9734540416718881

13072FE1AEFD99__

2017-12-19T12:35:54

kkmrkkblmbrbk

c4.xlarge

161456346886729

9734540416718881

13072FE1AEFD99__

2018-11-17T05:42:56

Oliver Kruse

GTX-7

161456346886729

9734540416718881

1073241228883391718769

13072FE1AEFD99__

2020-11-18T03:57:34

arnaud

SRV-130

161456346886729

9734540416718881

1073241228883391718769

79756687312821920818433

13072FE1AEFD9996

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 = 1010447130 (P-1 stage 2)

B1 = 1000000, B2 = 431367300 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 373713, B2 = 3737131 (P-1 stage 2)

B1 = 373713 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

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10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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10¹³

TF factor-bounds graph:

2⁶⁸

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-21T14:12:59+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