Wagstaff Conjecture

[science_man_88]

that's the lower ? limit: if so:

1.048160763796310932532406940721790497083607972712230068811827915593117475301021216847333399205353891

looks to be the lower limit to put my lowest value >=1.

[science_man_88]

scratch that:

(12:42)>for(n=1,#mersenne,print(solve(x=1,20,(mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(1.78)*1.78^exp(-Euler)^-x/log(mersenne[n]))-1)))
1.221045211781039641218621908242613887816818178982651231266946543163325501217342917242414949318615982
1.021017745318224477002391158250826730797295442352557610947905198183666740778662586872855983175813252
  ***   roots must be bracketed in solve.

[science_man_88]

(12:47)>for(n=1,#mersenne-1,print(solve(x=-10,10,(mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(1.78)*1.78^exp(-Euler)^-x/log(mersenne[n]))-1)))
1.221045211781039641218621908242613887816818178982651231266946543163325501217342917242414949318615982
1.021017745318224477002391158250826730797295442352557610947905198183666740778662586872855983175813252
0.6549826526828368183577151707013114476748827930307909955627869130134989722596480676067957138712436359
0.9987908631648755228843447478876116530237200051899251635379003240772227036148421501457988525719941289
0.4052267409168582888557720113896567274771705650312627259856272581089601184003426228756458463566985823
-0.2866708316919592079782584066540847186281803381515177809526170130611131969403186447856222985025989700
0.4585924665831132593559712551865244429861339513204641936987908996902917223088375207974204407982696379
0.8812716462927890695127651513577201383048362176484426831542438569555556586645618538284500589636209338
0.3894820394358417717882636151059958816021887252223221628901103615386542468234250470314224125094088048
-0.2094361779115823418749377454312584518122495166568803485690069767173075374474403785073503083941553317
-0.4565748594144080289308865882770544075881733796602817604897233171891542356582463687506800151766103368
1.802676985070192364236291634996266717393158714633447637842856991558141656783517508496735756415741539
-0.08460929481393289547305879169716849544194692984047134800924735037673752175791358587908620726759709019
1.105822037275535702621814976926679054427928363977232513618245760246767865969614120174322950405157507
0.8302552218662819564095079581592628828735409165696738304701253833034419310308169751230714801063203585
-0.5046186967007588544100286274646138297173416044719733546677081206407616685484030093150766224083933355
0.2954641445452101711602697484953234902580106697707754300431403328674064495406505543316926988014964098
0.08475732322566423726559129084205305683678916097981305339830979320151514558570012428997353114296053901
-0.8875319995143233762444648562162906385319714134823684610953349528065312604856263944006909492086661117
1.028169204353676486599126023019159204530072308358009475702504998702694435767081738473698432575553387
-0.9888062939148641485481861216604714156952458328115130728515631937789640132010533343024139310369132511
-0.7368703356932631210345030086071880547603359848230421721811351802618504119540097659716502610814991835
0.5683329567095742420406774543620266819730021976345398232299142253581679023843733845883850082130306219
-0.9821679292545116769946341777314225358285309606415429976762457359204070183074887668033506749254657242
-1.268904636516073103396990120185290738484991997369220562293511562652723340628743934332271626324966429
0.6276790240689950601167375641820574404430217984981715382984966870980614605703136710711345637484109953
0.7011070092533118566610212108127056572319364017177112306959442850371015195010044341153779254290974620
-0.3394997457980279553008155334939283556397368147517236660770767685747590965853981371631875636560896678
-0.6741435834117947628323563624449849583551324932975127968194894443603014928798985181167684369077619735
0.3020949811101398107195479487370099017075510194248465495780907217102916551504895411862495239334285646
1.604155614927746943000825384834664530528576584626099186809254228263545469673698550461399915901145249
-0.6570965048910669837506915423124464056158817333913983323892160003619129439702112150676220807592471279
0.1448437285612943760361273317280353061877907856078652552830946527897401846633685644682367731379907960
-0.8670062813180255889705213111866279285822129634331884725686760824811247641748921080636726065694112233
0.9146790096275647001143972092585110719899471107438132077369405902123919083845771412748335952529628693
-1.372481449062038178021845005155532039441680318815793705773837636591249887482146733324192978436146724
1.048160763796310932532406940721790497083607972712230068811827915593117475301021216847333399205353891
0.7824151999928314004404512647847017808565429525598779470151978973509417460821627602045802971003505457
0.3521336181631540101393215503335012764245324529017577484906998213110171395661319304476910513927703884

I'm worried what the negatives imply.

[science_man_88]

when I vecsort v and plot it it looks more solvable from my point of view:

(13:05)>plot(x=1,#v,v[floor(x)])

1.6041556 |'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''""
          |                                                              |
          |                                                           __ |
          |                                                          _   |
          |                                                   xxxxx""    |
          |                                              __x""           |
          |                                           _""                |
          |                                      _""""                   |
          |                                  __xx                        |
          |                            _xx"""                            |
          |                          __                                  |
          |                        ""                                    |
          ````````````````````````x```````````````````````````````````````
          |                   __xx                                       |
          |                  "                                           |
          |              xx""                                            |
          |           __x                                                |
          |         ""                                                   |
          |    __"""                                                     |
          |   "                                                          |
          |                                                              |
-1.372481 __""...........................................................|
          1                                                             39

[CRGreathouse]

Originally Posted by science_man_88

I'm worried what the negatives imply.

Those are numbers where the exponent -x is positive. The positive values are where the exponent -x is negative.

[science_man_88]

Originally Posted by CRGreathouse

Those are numbers where the exponent -x is positive. The positive values are where the exponent -x is negative.

is there anyway to make the graph more linear if we can get to linear then it's just a matter of predicting where it falls on that line.

[CRGreathouse]

Originally Posted by science_man_88

is there anyway to make the graph more linear if we can get to linear then it's just a matter of predicting where it falls on that line.

No, it really wouldn't be.

[science_man_88]

Originally Posted by CRGreathouse

No, it really wouldn't be.

well if we could predict the line and what to check we could use the formula's to convert it to the exponent correct ?

[CRGreathouse]

Originally Posted by science_man_88

well if we could predict the line and what to check we could use the formula's to convert it to the exponent correct ?

It's the first part, not the second, that gives trouble.

[science_man_88]

Originally Posted by CRGreathouse

It's the first part, not the second, that gives trouble.

what says we can't do something like what we've been doing to get the line, assuming that's the part you mean.

[science_man_88]

(13:04)>plot(x=1,#v,v[floor(x)])

 1.802677 |''''''''''''''''''"'''''''''''''''''''''''''''''''''''''''''''|
          |                  :                              xx           |
          |                  :                              ::           |
          |                  :                              ::           |
          ""                 :  __                          ::           |
          | xx xx            :  :         xx                ::        "" |
          |     :     xx     :  : _       ::               : :     "" :  |
          |   _  :    ::     :: : :       ::          _    : :     :: : ""
          |      :   :  :   : : : :       ::   xx   "":    : :     :: :  |
          |      __ xx  _   : ::  :       ::   ::   : :    :  :    :: :  |
          |       : :   :   : ::  :  xx   ::   ::   : :    x  :    :: :  |
          |       : :    :  : ::   : : _  ::   ::   :  :   :  : x  :: :  |
          ,,,,,,,,,:,,,,,:,,:,::,,,:,:,:,:,,:,,::,,,:,,:,,,:,,:,:,:,:,:,,,
          |        :     __ : ""   ::  : :  : : :   :  :   :  : : : ::   |
          |        x        :      ::  : :  : :  :  :  __ :   ::: :  :   |
          |                xx      __   ::  : :  : :    : :   :: ::  :   |
          |                             ::  : :  : :     ::   __ ::  :   |
          |                             ::  :xx  : :     ""      ::  :   |
          |                             xx  :    : :             xx  :   |
          |                                 "    " :                 :   |
          |                                        :                 :   |
-1.372481 |.......................................""................._...|
          1                                                             39

Here's the plot of v before organizing it numerically if it helps.