M1675771 Mersenne number exponent details

is 2 ^1675771 - 1

has 504458 decimal digits

takes 0.079 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	17.7315	68.6567%	500000	15000000	0.0880	5.0151%	17.8195	70.2286%	1.5719%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5712%	0.0124	64.1052%	0.9473%
GPU72	2⁶¹	0.1833	65.5738%	7000	90000	0.0008	1.2547%	0.1841	66.0057%	0.4320%
Difference	+6	+17.5482	+3.0829%	+493000	+14910000	+0.0872	+3.7603%	+17.6354	+4.2229%	+4.2229%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1675771	1756208009	10	30.710	524 2² × 131	-	4	131	9.504e-11	7.451e-7	9.387e-7
1675771	2519558565463	13	41.196	751761 3⁴ × 9281	2008-07-15	81	9281	3.005e-7	3.973e-5	6.444e-5
1675771	8898907069057	13	43.017	2655168 2⁶ × 3 × 13829	2008-07-15	64	13829	1.197e-6	5.554e-5	9.600e-5
1675771	170177523055941017	18	57.240	50775888548 2² × 7 × 11 × 349 × 472369	2015-05-02	349	472369	0.0122	0.0018	0.0033
1675771	267763018085696484193	21	67.860	79892484738576 2⁴ × 3 × 1664426765387	2018-02-08	16	1664426765387	25.052	6,188.2	11,558

exponent	prime factors	composite factor	digits	bits*
1675771	1756208009 2519558565463	4424868931810671393167	22	71.906
1675771	1756208009 8898907069057	15628331866024619477513	23	73.727
1675771	2519558565463 8898907069057	22421317529101804796178391	26	84.213
1675771	1756208009 170177523055941017	298867128942625769087005153	27	87.950
1675771	2519558565463 170177523055941017	428772235864873356692061295871	30	98.436
1675771	1756208009 267763018085696484193	470247556876112013882888501737	30	98.569
1675771	8898907069057 170177523055941017	1514393962917124117442537810969	31	100.257
1675771	2519558565463 267763018085696484193	674644605732040758112537735226359	33	109.056
1675771	8898907069057 267763018085696484193	2382798214474841783004419159916001	34	110.876
1675771	1756208009 2519558565463 8898907069057	39376497416940680159403102866933519	35	114.923
1675771	170177523055941017 267763018085696484193	45567247183806964956476648418080844281	38	125.099
1675771	1756208009 2519558565463 170177523055941017	753013234662727630793311794527568830839	39	129.146
1675771	1756208009 8898907069057 170177523055941017	2659590806456302378299641500909085850721	40	130.966
1675771	1756208009 2519558565463 267763018085696484193	1184816259815257287311670493919253103709231	43	139.766
1675771	2519558565463 8898907069057 170177523055941017	3815604280753296860101040503339189905963647	43	141.453
1675771	1756208009 8898907069057 267763018085696484193	4184689308091616868320201011037532723452009	43	141.586
1675771	2519558565463 8898907069057 267763018085696484193	6003599651050030164690507472747511071139673463	46	152.073
1675771	1756208009 170177523055941017 267763018085696484193	80025564452284486966546626373310759135774046529	47	155.809
1675771	2519558565463 170177523055941017 267763018085696484193	11480934794653060330884821651911798028819624766710 3	51	166.296
1675771	8898907069057 170177523055941017 267763018085696484193	40549869808144747587210232094360646154550973051301 7	51	168.116
1675771	1756208009 2519558565463 8898907069057 170177523055941017	67009947970336244988639998811976765564253137242488 23	52	172.163
1675771	1756208009 2519558565463 8898907069057 267763018085696484193	10543569790003668234921058229913528177951663293365 365167	56	182.782
1675771	1756208009 2519558565463 170177523055941017 267763018085696484193	20162909637176474929460113841624109859803437831671 3854427927	60	197.005
1675771	1756208009 8898907069057 170177523055941017 267763018085696484193	71214006120971099143942035570865010511037470671439 2134153153	60	198.826
1675771	2519558565463 8898907069057 170177523055941017 267763018085696484193	10216777180352059526428964286186259167732219705004 84831568131871	64	209.312
1675771	1756208009 2519558565463 8898907069057 170177523055941017 267763018085696484193	17942785910302724379959294248975276416120998613277 13199582969221018354839	73	240.022

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2015-05-02T13:08:00	alpertron	Manual testing	500000	15000000	12		170177523055941017	18	57.240	0.034	0.158	0.068	5.015%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:45:00	J Feitsma	Manual testing	?	?	2519558565463	41.196	13	1.25663e-7	0.172	2.73697e-7
2008-07-15T07:45:00	J Feitsma	Manual testing	?	?	8898907069057	43.017	13	4.97655e-7	0.172	1.08390e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.897 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.897 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	14.72
50000	5000000	267763018085696484193	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-09-19T20:54:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-02-08T14:25:46	Chang Chia-Tche	exbpc13	50000	5000000	267763018085696484193	67.860	3	2		3	0.178
2019-03-24T10:48:28	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-01-13T11:53:08	TJAOI	Manual testing	50000	5000000						244	14.48

Lucas-Lehmer results:
No L-L results for M1675771

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T23:41:07

Oliver Kruse

GTX-1

1756208009

2519558565463

8898907069057

170177523055941017

79CB631E963BCF8F

2017-10-03T00:14:33

kkmrkkblmbrbk

Manual testing

1756208009

2519558565463

8898907069057

170177523055941017

79CB631E963BCF__

2017-11-14T10:12:45

ATH

ec2-1xf

1756208009

2519558565463

8898907069057

170177523055941017

79CB631E963BCF__

2018-02-10T21:40:19

Oliver Kruse

GTX-5

1756208009

2519558565463

8898907069057

170177523055941017

267763018085696484193

D25156BF8BE3D6__

2018-02-11T09:55:53

kkmrkkblmbrbk

c5.large

1756208009

2519558565463

8898907069057

170177523055941017

267763018085696484193

D25156BF8BE3D6__

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

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10³

10⁴

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10¹³

TF factor-bounds graph:

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-01-13T11:53:08+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