M1759271 Mersenne number exponent details

≡

M1759271

<<<

>>>

is 2 ^1759271 - 1

has 529594 decimal digits

takes 0.095 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	2⁶⁷	16.8899	68.6567%	500000	15000000	0.1015	5.0446%	16.9914	70.2378%	1.5811%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8053%	0.0121	64.1914%	1.0335%
GPU72	2⁶¹	0.1746	65.5738%	8000	110000	0.0011	1.4142%	0.1757	66.0606%	0.4869%
Difference	+6	+16.7153	+3.0829%	+492000	+14890000	+0.1004	+3.6303%	+16.8157	+4.1772%	+4.1772%

Known prime factors (4 factors, 163.2 bits, 0.00927524% 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
1759271	14074169	8	23.747	4 2²	-	4	4	6.358e-13	3.146e-7	6.404e-7
1759271	2702240257	10	31.332	768 2⁸ × 3	2008-07-15	256	256	1.896e-10	2.014e-5	4.098e-5
1759271	130414759231	12	36.924	37065 3 × 5 × 7 × 353	2008-07-15	7	353	5.322e-9	2.034e-6	2.852e-6
1759271	2664168214746469141457	22	71.174	757179597329368 2³ × 61 × 1551597535511	2020-05-25	61	1551597535511	442.86	6,649.8	12,420

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1759271	14074169 2702240257	38031786055621433	17	55.078
1759271	14074169 130414759231	1835479361511404039	19	60.671
1759271	2702240257 130414759231	352412012500970562367	21	68.256
1759271	14074169 2702240257 130414759231	4959906221568772358778198023	28	92.002
1759271	14074169 2664168214746469141457	37495953698770098850150724233	29	94.921
1759271	2702240257 2664168214746469141457	7199222601307729962653333034449	31	102.506
1759271	130414759231 2664168214746469141457	347446856277043876790485935539567	33	108.098
1759271	14074169 2702240257 2664168214746469141457	101323075559424612500746697540118047881	39	126.252
1759271	14074169 130414759231 2664168214746469141457	4890025773761826342364476648906972144823	40	131.845
1759271	2702240257 130414759231 2664168214746469141457	938884882199921108818599049607324963748719	42	139.430
1759271	14074169 2702240257 130414759231 2664168214746469141457	13214024503626781472180353367412875177718344739511	50	163.177

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:30:08	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 14074169 skipped known factor: 2702240257 skipped known factor: 130414759231	-	-	0.101	-	-	5.045%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	130414759231	36.924	12	1.18266e-10	0.205	2.53837e-10
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	2702240257	31.332	10	2.70321e-11	0.205	5.80199e-11

ECM factoring results:

Old Calculation Method

Total ECM effort:

23.106 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	336 / 100	3.360	3.415%
25	50000	336 / 280	1.200	30.055%

New Calculation Method

Total ECM effort:

23.106 GHz-days

Digits	B1	Complete	FacMiss
20	11000	10.839	0.002%
25	50000	0.980	37.546%
30	250000	0.060	94.146%
35	1000000	0.003	99.724%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	17.26
50000	5000000	2664168214746469141457	85	5.845

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-04T11:33:06	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-22T06:00:39	Oliver Kruse	ECM-HTC	50000	5000000						3	0.206
2019-08-02T13:46:55	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-27T17:48:19	kracker	O0	50000	5000000						3	0.206
2020-03-09T06:25:10	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-22T06:58:32	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-30T00:58:09	Greg	azure4	50000	5000000						3	0.206
2020-05-25T17:32:29	nordi	sweet16	50000	5000000	2664168214746469141457	71.174	85	2	459347924097871	85	5.845
2020-08-21T10:53:56	TJAOI	Manual testing	50000	5000000						232	15.95

Lucas-Lehmer results:
No L-L results for M1759271

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T08:58:17

Oliver Kruse

GTX-3

14074169

2702240257

130414759231

35AD7B5536F050__

2017-11-03T23:48:56

ATH

ec2-1xf

14074169

2702240257

130414759231

35AD7B5536F050__

2020-05-27T17:24:00

Luigi Morelli

9800X

14074169

2702240257

130414759231

2664168214746469141457

9B1767F18626B6FE

2020-05-29T19:09:18

arnaud

stm-11-010

14074169

2702240257

130414759231

2664168214746469141457

9B1767F18626B6FE

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-21T10:53:56+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