Wagstaff Conjecture

[science_man_88]

now I've got it to 1.8026486875969201048629953936014631

with closest to 1 answer of:

0.9999999999999999999999997503263465181800920351371235523412918875090130628069254608685016146340307958 by the looks of it.

[CRGreathouse]

If you want to find the limiting value, just solve algebraically (or, for that matter, use solve()).

[science_man_88]

Originally Posted by CRGreathouse

If you want to find the limiting value, just solve algebraically (or, for that matter, use solve()).

that's the high limiting exponent I'm finding right now how would I use solve ?

[retina]

Originally Posted by science_man_88

now I've got it to 1.8026486875969201048629953936014631

with closest to 1 answer of:

0.99999999999999999999999975<snip excessive digits> by the looks of it.

Truly amazing. I just made that number up. I must be a genius at typing numbers randomly!

[science_man_88]

Originally Posted by retina

Truly amazing. I just made that number up. I must be a genius at typing numbers randomly!

must of mis quoted the number lol.

(10:02)>for(n=1,#mersenne-1,print((mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(1.78)*1.78^exp(-Euler)^-1.802676985070192364236291639/log(mersenne[n]))))
0.6278314343193879400011266570861233450358404854870381898972466355615955230896054428093709889780811741
0.5528273778723374597913496790476980080262340314791171244906423400659886013727794355361668713866124222
0.4535313832621029429682183518938119599837053456206636162935340713111564556297628594616085349494922052
0.5455498494206487761009186503033516504072777697706710242213303186807849693040016283250745450417362321
0.4050799014307713836828705163107088850296716817150577267847947092194201251454047338052710434488327035
0.3186831078995988518105244192073779471336389224410223411924615068234313373592501989815614854319984612
0.4144183214694355823075087290774112713198557643966975427904436036429888622252096834091240376856827533
0.5100387384474481241253389951078340714950810714461163095844147772722125120125510460410488712230512153
0.4024186961748819543401228370275124179668777137285639384027893112423369858060634753159836383725880416
0.3258626096486891232692313018532754534402299418582458820615134709770647955331199034805065522535022870
0.3044622603857871978440340311724219178077481127255691830161080022262318074175821935243174451102993515
0.9999999999999999999999999962278768534585812009422486238241359114819840803301054876132222288992428642
0.3385426107588963136984776734652464435064968458791733881695831703013568859572337114395943293002333993
0.5824229685955660712434907257539212970218734242168202099641132285093140341983908844241759823258589745
0.4960413446365699555661682160981404096414991551491957287594964127824155447350092937853292711152383897
0.3007953306080179379444070410874314037344366359931109120537832795915764932940607271487015377995027888
0.3873608934977556845868625313811233191869481911606533268265200597652803358703582062624776114719424189
0.3581834057516558931390338750087985168970729977691165898566827791617369283115785270693583139452496091
0.2761598210483672495081375783524145768285971779204348953592191737127044171433573473496754693719670714
0.5552096319958394086996086293827763104300260570903597419332413711517028677663011921842116036405522111
0.2707955572370063167689267755273516266866091619222618325425300487121766594553355736335367574242566854
0.2849652923003854276696423861350316392275559011314549807029271404260857967540372598638645848628854963
0.4352886746147908003432497074466101003316002195510478986519527173973633328867099990394066847830203183
0.2711345215082815504090609938096468780274898558458925681880938278614898958708352853602116368075758938
0.2579384110116061589094167676065351567263081202664564065241961289975491145140118143351026383020841556
0.4476025317344592071212359981423460194123457382820176488141455766936817669665463738994882667817350791
0.4639470364907654555889243792169059001091476117145820889270834668245518998139976676878902221558307731
0.3140400664712936584957219539132716659076205169778088899679298796684284404306198718844531519515015088
0.2889523667411004828447380629006258301585662154447923491576332080691412791674020197315594069023959858
0.3883780206950100593261583378560284833509776163417596475996633337903499552225744369891671800938120573
0.8380154038415163178175557048457458506662215183023190768234323822159015361654035461547146766363584387
0.2900709836639948590597102291999609214387316329591842244898159195508121239468601681026068870882613265
0.3659200617068177975269204801846481491539343799475547205433085216300976016924740638369950918203290340
0.2772991873060759830741564408140379506396506003472284719989722918743135071415523070070319826803310797
0.5196513531575771352023578778937314686208013891407417592078924606166712071203601925812551684931265513
0.2538221390563445814674882292986476477656158594062568225245371882452430373342228056977031700940179021
0.5619768645591646499521610943222827535333882379767904599064054333669492153199395096056139612098484764
0.4836195635660981519934262266143783784731246593186644421448212669880914733973344257417120939659363426
0.3962698020212401052924875800234991883491429938337654299871024276756786674616112811411193012681299510

as you go down in the number the answers rise we want the highest (#12 in this list) to just barely be under 1. then we can start on a exponent for a limit to stay above where they all are above 1.

[science_man_88]

-1.80267698507019236423629163499626671739315871463345 is my closest so far now :

#12 = 0.9999999999999999999999999999999999999999999999999977744902055241948890317038784593675635703070953915

[CRGreathouse]

Originally Posted by science_man_88

that's the high limiting exponent I'm finding right now how would I use solve ?

Take the term that is closest to the limit (#12) and solve the equation that_term = 1.

Or in gp, assuming the formula for term t is in a function f(x, t),

solve(x=-2,-1,f(x, 12)-1)

[science_man_88]

Originally Posted by CRGreathouse

Take the term that is closest to the limit (#12) and solve the equation that_term = 1.

technically for a lower limit I'd want .99999999999.....................................

and for an upper limit equation we'd want on that brought everything above 1 just barely but I can't find that one in my current setup and I've got it as low as -((1*10^-10000000)*Euler)

[science_man_88]

I don't see how I can use solve I tried:

solve(x=1,10,7==6*x+1)

and it gave me back 10 when the answer is algebraically 1.

[CRGreathouse]

solve() tries to find a value that makes the formula you give equal to 0. 7==6*10+1 is the same as 7==61 which is 0 (false), so it's a valid result.

What you should have done to solve the equation 7 = 6x + 1 is

solve(x=0,9,6*x+1-7)

This is stated clearly in the help:

> ?solve
solve(X=a,b,expr): real root of expression expr (X between a and b), where
expr(a)*expr(b)<=0.

[science_man_88]

Originally Posted by CRGreathouse

solve() tries to find a value that makes the formula you give equal to 0. 7==6*10+1 is the same as 7==61 which is 0 (false), so it's a valid result.

What you should have done to solve the equation 7 = 6x + 1 is

solve(x=0,9,6*x+1-7)

This is stated clearly in the help:

> ?solve
solve(X=a,b,expr): real root of expression expr (X between a and b), where
expr(a)*expr(b)<=0.

solve gave back this at precision set to 100:

1.802676985070192364236291634996266717393158714633447637842856991558141656783517508496735756415741539