M3103483 Mersenne number exponent details

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M3103483

<<<

>>>

is 2 ^3103483 - 1

has 934242 decimal digits

takes 0.264 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	2⁷⁰	76.9943	68.5714%	3103483	3117527490	21.3237	10.7294%	98.3180	71.9435%	3.3721%
PrimeNet	2⁶⁰	0.0495	63.3333%	12000	220000	0.0029	2.5309%	0.0524	64.2613%	0.9280%
GPU72	2⁶⁴	1.1469	65.6250%	14000	240000	0.0032	1.5074%	1.1501	66.1432%	0.5182%
Difference	+6	+75.8475	+2.9464%	+3089483	+3117287490	+21.3205	+9.2219%	+97.1679	+5.8003%	+5.8003%

Known prime factors (4 factors, 180.1 bits, 0.00580224% 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
3103483	347590097	9	28.373	56 2³ × 7	-	8	8	1.166e-11	9.873e-7	2.009e-6
3103483	4077976663	10	31.925	657 3² × 73	2008-09-07	9	73	1.053e-10	1.541e-6	2.260e-6
3103483	4553628880513	13	42.050	733632 2⁶ × 3 × 3821	2008-09-30	64	3821	3.388e-7	3.316e-5	4.798e-5
3103483	249477522902369776763071	24	77.723	40193151195345645 3 × 5 × 7 × 23 × 1058507 × 15723209	2018-07-16	1058507	15723209	18,156	0.2292	0.2659

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3103483	347590097 4077976663	1417464303855906311	19	60.298
3103483	347590097 4553628880513	1582796304279515079761	22	70.423
3103483	4077976663 4553628880513	18569592306694829468119	23	73.975
3103483	347590097 4077976663 4553628880513	6454606391134509524221941617543	31	102.348
3103483	347590097 249477522902369776763071	86715916384954432234944194907887	32	106.096
3103483	4077976663 249477522902369776763071	1017363516338911977036323218212073	34	109.648
3103483	4553628880513 249477522902369776763071	1136028053327074405156388718569935423	37	119.773
3103483	347590097 4077976663 249477522902369776763071	353625483328503498972517359941686620641081	42	138.021
3103483	347590097 4553628880513 249477522902369776763071	394872101250678965214526454857429554964306031	45	148.146
3103483	4077976663 4553628880513 249477522902369776763071	4632695889981128930292360059684671388411033449	46	151.699
3103483	347590097 4077976663 4553628880513 249477522902369776763071	16102792137700419330498276715047207173109157924081 54553	55	180.071

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-02T21:53:04	Jocelyn Larouche	Manual testing	3103483	3103483		-	skipped known factor: 347590097 skipped known factor: 4077976663 skipped known factor: 4553628880513	-	-	0.383	-	-	3.085%
2022-01-02T23:44:20	Jocelyn Larouche	Manual testing	3103483	116689650		-	skipped known factor: 347590097 skipped known factor: 4077976663 skipped known factor: 4553628880513 skipped known factor: 249477522902369776763071	-	-	1.147	-	-	7.021%
2022-08-04T01:56:28	Jocelyn Larouche	Manual testing	3103483	3117527490		-	skipped known factor: 347590097 skipped known factor: 4077976663 skipped known factor: 4553628880513 skipped known factor: 249477522902369776763071	-	-	21.32	-	-	10.729%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:46:00	markr	Manual testing	?	?	4553628880513	42.050	13	1.50050e-7	0.586	3.32875e-7
2008-09-07T19:44:00	Will Edgington	Manual testing	?	?	4077976663	31.925	10	1.31089e-11	0.586	2.90813e-11
2021-01-04T13:51:30	Jocelyn Larouche	Manual testing	2⁶⁰	2⁶¹		-	-	0.049	-	-
2021-01-05T04:03:49	Jocelyn Larouche	Manual testing	2⁶¹	2⁶²		-	-	0.099	-	-
2021-01-06T02:31:34	Jocelyn Larouche	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2021-01-07T23:43:18	Jocelyn Larouche	Manual testing	2⁶³	2⁶⁴		-	-	0.633	-	-
2021-01-14T02:35:50	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵		-	-	1.204	-	-
2021-02-04T11:55:01	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.408	-	-
2021-02-06T11:14:31	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.816	-	-
2021-02-06T18:57:49	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.63	-	-
2021-09-04T19:50:29	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.26	-	-
2021-11-16T12:13:08	Jocelyn Larouche	Manual testing	2⁶⁹	2⁷⁰		-	-	38.53	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	249477522902369776763071	3	0.350

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-07-16T10:06:40	ATH	ec2-ECMCF	50000	5000000	249477522902369776763071	77.723	3	2		3	0.350

Lucas-Lehmer results:
No L-L results for M3103483

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-29T18:30:45

Oliver Kruse

GTX-2

347590097

4077976663

4553628880513

DB6023402B5C2D__

2017-12-11T19:35:55

kkmrkkblmbrbk

c4.xlarge

347590097

4077976663

4553628880513

DB6023402B5C2D__

2018-07-16T10:52:59

ATH

ec2-PRPCF

347590097

4077976663

4553628880513

249477522902369776763071

DB6023402B5C2D__

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 = 3103483, B2 = 3117527490 (P-1 stage 2)

B1 = 3103483, B2 = 116689650 (P-1 stage 2)

B1 = 3103483 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-04T01:56:28+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