Wagstaff Conjecture

[science_man_88]

for exponent on the supposed unimportant part Pi seems to me a better base than exp(1) because it works for all exponents <=0 in the to make all results below 1 I believe. Sorry in the 2^Pi^(-Euler)^0 part.

[CRGreathouse]

Why stop there? Use a billion and be really sure... or at least expand the SLSN range.

[science_man_88]

Originally Posted by CRGreathouse

Why stop there? Use a billion and be really sure... or at least expand the SLSN range.

? I was thinking of shrinking ranges to check but okay lol.

[CRGreathouse]

That's my point -- you want to shrink, not grow, so going up to pi is the wrong direction. You should be able to find your answers in the Poisson model -- and this is an extremely simple model, one of the easiest to use in all of probability.

[science_man_88]

Originally Posted by CRGreathouse

That's my point -- you want to shrink, not grow, so going up to pi is the wrong direction. You should be able to find your answers in the Poisson model -- and this is an extremely simple model, one of the easiest to use in all of probability.

have the exponentials on either side of the gaps been mapped ? if so that's what to stay in hopefully , if I knew more about plotting in PARI I may be of help.

[science_man_88]

Originally Posted by CRGreathouse

That's my point -- you want to shrink, not grow, so going up to pi is the wrong direction. You should be able to find your answers in the Poisson model -- and this is an extremely simple model, one of the easiest to use in all of probability.

(14:24)>for(n=1,#mersenne-1,print((mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(2)*2^exp(-Euler)^-2/log(mersenne[n]))))
0.2963737791339523749176256911233465807543806849468041682722902996028611886354097380464620338685406412815327253126366005
0.2609674034024048743742401206425696136839286562900917399431561009334242770791062479357653399795163432392668807276326004
0.2140937880228205150022807312053548222253850551733027987966115660483195701750173132730933105488680745655127861972304428
0.2575319771206354231598192040139034640489211651146282983611461329063074846130531309082478251779453413957810592380695700
0.1912218068029589893664201617069420196864101716557602530854103335472188671877746496207182749436838920601394291433567664
0.1504373815509042161971784085363214617350508688745349416304816141331881977602445632755812420106228887353209802860231448
0.1956300964914156900515019012112605777770955104069989794016155952223533669407898427318608411753515168937779512484173403
0.2407686206127186362161410689718896127374772998510014101609805848938705510178714395712842933218368965062257326185242952
0.1899655596391098203379716293254193253631314548521767063693736802432312085794234223559835319959786372266643649649244329
0.1538265333986185672555808013269594235262555942619193828355570665374601884866839551224388485632503861628805179051356572
0.1437242956973342399345958634500339643592989122364654180462440924397269728504653378309355401019046798255938873109785670
0.4720594779636061846065870390565873763960551848167949538836339626629930271054328335063581567499357698811008775986601773
0.1598122481032809204218642875843951874815286211966726961064586374541305659995501729108224781517096288456314372126605112
0.2749382825092367187057624579205920100079466034438123868416707651279433672623083249663964867624561165928987101909952785
0.2341610181975044758108449000935054321650597688414486785301434847165285159093452586868088085454451120928059254697986735
0.1419932867407112806673243573681903055212501312699551850842202529015297169115525078654601115672703181172378086075706588
0.1828573811680666017890221535466016526850829155247655615189095224630490754873753944861494948801767685989216836167566071
0.1690838715343532178049264183626593743165356243107049174568735526336946440702496228140263890843370718559369196578811457
0.1303638609586151470087949458580743384454010899510975328807177160754717975296815516330252673756589757086122112545030395
0.2620919690403218525910645839016634181692803754183973653442097924877718672281857885683657861965591370391537930715364147
0.1278316093841650406572022197286096136846753666849667800676935285249588361402583793723131543190186386265073937751347000
0.1345205671210663899430279506597010776477889887211284506111231476399941305462058555451987783697870026593606903402263986
0.2054821445021281806224625794992707248706625033509951848483547329994160371960934051363852695168298527375733236459195387
0.1279916206811115416405782650566943118625862995242183705703157175940676188088429480985846219804337941196518214989599884
0.1217622716489008924031376576427657367455059532114132333594561829407288483551577746423307141686631867211627316723193768
0.2112950174657572840163763739504773027947006580635376038836471856336528463416153750232336730951175538988866629328779359
0.2190105958485928899873738813148940145547242078605902639577025543044913780552080585849124341377811151339758568558019572
0.1482455898380950702089093747333354613548758628162764375904242320558063756400580319708957830923414532739233111620284336
0.1364027034001523759845696354938431142026758763799969081582664220185849076990048546297993130096969079225173910367929511
0.1833375257018250878222220227960150460013749061727937559152184110538088397507220230468475908538738721498793674525955127
0.3955931140628868098131928912260168566412772140503285777834736997349615242969187937515554035723378176348137467676718165
0.1369307571208151507319572465153229299112338971178110511796858722790521727903031921595043707256874947663853476332108428
0.1727360333057309713671635673684782895521255565320554182354115293612432073228552645547576717454834524732887400978773024
0.1309017095994384793667623531855607056592029666110528881775568719526883340394935548741353745339624078369967178397511795
0.2453063464946474187726063795222703503534110623424408691432390357941609899091277321884348969143197607027906940500363189
0.1198191464585438796440931693925091566225045236292939820278828490354990178729923487511841590242709160129641820295836809
0.2652865053114234825083346150655640895711909267525972528117432735523063476968035042007450460109941675046671710497112875
0.2282971987099993510097139239400680459571610576648090047769432571512328727979790574615952408980953656365447663086499610
0.1870629158748881789962914104447693092658399913065539884562370962789111802762896359808781584589557132477886591090097027

these are below 1 so they represent the high range that I can find so far. but I'd like a expression that gives closer to 1.

[science_man_88]

UPDATE: I've changed 2 in the previous code to

but I can see i negative to it so I might change one back to make sure it works more.

[science_man_88]

for(n=1,#mersenne-1,print((mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(1.78)*1.78^exp(-Euler)^-1.8027/log(mersenne[n]))))

closest I can get right now.

[CRGreathouse]

Originally Posted by science_man_88

closest I can get right now.

Closest to what?

As for graphing in gp, the main command is ploth, as in

ploth(x=1,10,x^2)

though if you don't have the high-resolution graphics compiled in you can only use plot instead.

[science_man_88]

Originally Posted by CRGreathouse

Closest to what?

As for graphing in gp, the main command is ploth, as in

ploth(x=1,10,x^2)

though if you don't have the high-resolution graphics compiled in you can only use plot instead.

the values I get back are under 1 if i go any lower in the last digit of the last exponent

1.78^exp(-Euler)^-1.8026

gives over 1 for 1 value,

1.78^exp(-Euler)^-1.8027

makes them all below 1

[science_man_88]

Originally Posted by CRGreathouse

Closest to what?

As for graphing in gp, the main command is ploth, as in

ploth(x=1,10,x^2)

though if you don't have the high-resolution graphics compiled in you can only use plot instead.

Is there one where you can plot multiple expressions ? then we can plot the nearest path on either side. Or should I use open office if possible.