M1675769 Mersenne number exponent details

is 2 ^1675769 - 1

has 504457 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
1675769	120655369	9	26.846	36 2² × 3²	-	9	9	5.377e-12	6.142e-7	1.250e-6
1675769	2144984321	10	30.998	640 2⁷ × 5	2008-07-15	128	128	9.718e-11	8.735e-6	1.778e-5
1675769	16702916189838257	17	53.891	4983657112 2³ × 7² × 23 × 552757	2014-10-19	49	552757	0.0012	0.0021	0.0038
1675769	2090876525733448933703	22	70.825	623855831481979 23 × 31 × 53 × 739 × 22339549	2019-03-24	739	22339549	143.18	0.0831	0.1551
1675769	77881179333923777765799193	26	86.009	23237444819042415084 2² × 3 × 17789 × 108856806730013	2019-12-30	17789	108856806730013	14,744,280	404,723	755,909

exponent	prime factors	composite factor	digits	bits*
1675769	120655369 2144984321	258803874749469449	18	57.845
1675769	120655369 16702916189838257	2015296516261008948651833	25	80.737
1675769	2144984321 16702916189838257	35827493342180120790968497	26	84.889
1675769	120655369 2090876525733448933703	252275478745807276738592001407	30	97.671
1675769	2144984321 2090876525733448933703	4484897364845200988047103470663	31	101.823
1675769	120655369 2144984321 16702916189838257	4322779429545785738498875872910393	34	111.736
1675769	120655369 77881179333923777765799193	9396782430689747624206497211317217	34	112.856
1675769	2144984321 77881179333923777765799193	167053908572255726716727679019452953	36	117.008
1675769	16702916189838257 2090876525733448933703	34923735372625991177384370120686075671	38	124.716
1675769	120655369 2144984321 2090876525733448933703	541126946482525353091987858634024939647	39	128.669
1675769	16702916189838257 77881179333923777765799193	1300842811180292148281322535461461011126601	43	139.900
1675769	120655369 2144984321 77881179333923777765799193	20155950981677777869369936584605654222354657	44	143.854
1675769	120655369 16702916189838257 2090876525733448933703	4213736178242541464498055631743952993246427599	46	151.562
1675769	2144984321 16702916189838257 2090876525733448933703	74910864805035843672573803699332510077314554391	47	155.714
1675769	2090876525733448933703 77881179333923777765799193	162839929665738231007824995085047282767467901679	48	156.834
1675769	120655369 16702916189838257 77881179333923777765799193	15695366939395547467868568632411816357659314937076 9	51	166.747
1675769	2144984321 16702916189838257 77881179333923777765799193	27902874340672901622628439357088003686193656910229 21	52	170.899
1675769	120655369 2144984321 16702916189838257 2090876525733448933703	90383980351607127765407074650765290570746060891166 75279	55	182.560
1675769	120655369 2090876525733448933703 77881179333923777765799193	19647511801753692919656366669409566284756180872735 464551	56	183.680
1675769	2144984321 2090876525733448933703 77881179333923777765799193	34928909596575127640206064276932848307987213797222 4574959	57	187.832
1675769	120655369 2144984321 16702916189838257 77881179333923777765799193	33666315997345206535789331005235758502310558799631 0520712849	60	197.745
1675769	16702916189838257 2090876525733448933703 77881179333923777765799193	27199016975659821682586346283948080480722068176028 38722188733503	64	210.725
1675769	120655369 2144984321 2090876525733448933703 77881179333923777765799193	42143604761424131616511619213710510008212229279857 667842546304871	65	214.679
1675769	120655369 16702916189838257 2090876525733448933703 77881179333923777765799193	32817074296354998035866564852515344272432185222218 6201473170128447127607	72	237.571
1675769	2144984321 16702916189838257 2090876525733448933703 77881179333923777765799193	58341464959403156138803551507745246609194978996273 95864186508166782406463	73	241.723
1675769	120655369 2144984321 16702916189838257 2090876525733448933703 77881179333923777765799193	70392109826773578236919577256775090876284189837426 8410502497027684644794501249847	81	268.570

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:15	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 120655369 skipped known factor: 2144984321 skipped known factor: 16702916189838257	-	-	0.088	-	-	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	?	?	2144984321	30.998	10	1.18246e-11	0.172	2.57544e-11
2014-10-19T12:41:00	TJAOI	Manual testing	2⁵³	2⁵⁴*	16702916189838257	53.891	17	0.000	0.170	0.001

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		217	12.88
50000	5000000	2090876525733448933703	1	0.059
50000	5000000	77881179333923777765799193	33	1.959

	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
2018-02-08T13:34:38	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-03-24T09:57:25	Chang Chia-Tche	exbpc13	50000	5000000	2090876525733448933703	70.825	1	2		1	0.059
2019-12-30T12:50:20	TJAOI	Manual testing	50000	5000000	77881179333923777765799193	86.009	33	2		33	1.959
2019-12-30T12:50:20	TJAOI	Manual testing	50000	5000000						213	12.64

Lucas-Lehmer results:
No L-L results for M1675769

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T14:59:24

alpertron

Manual testing

120655369

2144984321

16702916189838257

9B6EA4C9750313__

2017-10-18T12:54:49

Oliver Kruse

Threadripper

120655369

2144984321

16702916189838257

9B6EA4C9750313__

2019-03-24T10:39:41

ATH

ec2-PRPCF

120655369

2144984321

16702916189838257

2090876525733448933703

A9991C4C590FB368

2019-03-25T07:58:36

marssystems

SYSTEM01

120655369

2144984321

16702916189838257

2090876525733448933703

A9991C4C590FB368

2019-12-31T03:04:15

Nagasan64

Core2

120655369

2144984321

16702916189838257

2090876525733448933703

77881179333923777765799193

A9991C4C590FB368

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

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁵⁴

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-12-31T03:04:15+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