[FOM] On the difficulty of finding a prime number just by guessing

[Joao Marcos]

Reply to Lindauer 1:06PM 6/21/03.

>For instance, is:
>
>123890164571029365109343456822478103948560192834750160594382741092845610
>923874109348564127893561024938750162938740213964501928734016503945817205
>961029387401928465019284730196509817230498162054938712043986102983570194
>283605981720398461095879042387501285630981712734891026509382741092856192
>837401928560192873410986598475192837409182605349857109238456019283741757
>283495621039874016501923874106539487120945610923874016520394871034650192
>834750165049871045610294857023946850198273409283645091823745092836405958
>712094651412845609387410926519283793685198237401938465067586405986985697
>459834659182734011001010109183274509236450179231010192939292929383883274
>929562973415610274938561029748374938759825691720394810365019283740165027
>493845682739481056029837492794723848472956105017514374589230645598127431
>752893468573940298364359827340659103847502638459713049623984752093861098
>273457171717172172717717727371727173727712171113123890164571029365109343
>456822478103948560192834750160594382741092845610923874109348564127893561
>024938750162938740213964501928734016503945817205961029387401928465019284
>730196509817230498162054938712043986102983570194283605981720398461095879
>042387501285630981712734891026509382741092856192837401928560192873410986
>598475192837409182605349857109238456019283741757283495621039874016501923
>874106539487120945610923874016520394871034650192834750165049871045610294
>857023946850198273409283645091823745092836405958712094651412845609387410
>926519283793685198237401938465067586405986985697459834659182734011001010
>109183274509236450179231010192939292929383883274929562973415610274938561
>029748374938759825691720394810365019283740165027493845682739481056029837
>492794723848472956105017514374589230645598127431752893468573940298364359
>827340659103847502638459713049623984752093861098273457171717172172717717
>727371727173727712171113
>
>Prime or not?


It is NOT:  97 is its first prime divisor, then 353, 449, 641, 1409, "and so
on". ;-)  Of course, guessing a divisor in such a case might not be worse a
method than systematically looking for one.  Even more obviously, I have not
found the above divisors "by hand", but I find no reason in this case not to
be fully confident about the ("mathematically certain"?) answers spit by the
software I used.  Or should I?


JM