The "Proth" program

and

the search for prime numbers

 

Yves Gallot

 

Or, pour comprendre une théorie, il ne suffit pas de constater que le chemin que l'on a suivi n'est pas coupé par un obstacle, il faut se rendre compte des raisons qui l'ont fait choisir. Pourra-t-on donc jamais dire qu'on comprend une théorie si on veut lui donner d'emblée sa forme définitive, celle que la logique impeccable lui impose, sans qu'il ne reste aucune trace des tâtonnements qui y ont conduit ? Non, on ne la comprendra pas réellement, on ne pourra même la retenir, ou on ne la retiendra qu'à force de l'apprendre par cœur.

Henri Poincaré, Œuvres, 1899.

To understand a theory, it is not sufficient to notice that the way we followed is not blocked by an obstacle, we should be aware of the reasons for which it was chosen. Will we ever be able to say that we understand a theory if we want to give to it straightaway its final form, that impeccable logic imposes on it ? Which ideas were tried out and discarded, which ideas were tried out and retained ? If we don't know these things we will not really understand it, we will even not be able to remember it; at best we will only remember it by learning it off by heart.

 

CONTENTS

 

History of the Proth program

History of the Proth program

History of the Proth program

History of the Proth program

History of the Proth program

History of the Proth program

 

Primality tests

Primality tests

Primality tests

Primality tests

 

Fast evaluation of tests

Fast evaluation of tests

Fast evaluation of tests

Fast evaluation of tests

 

Fast evaluation of tests

Fast evaluation of tests

 

Fast evaluation of tests

 

Fast evaluation of tests

Fast evaluation of tests

 

Fast evaluation of tests

a remark about the implementation

Fast evaluation of tests

a remark about the implementation

Actual searches for prime numbers

Actual searches for prime numbers

Actual searches for prime numbers

Actual searches for prime numbers

 

Search of tomorrow

Search of tomorrow

Search of tomorrow