
  !Primes+

 Important message:

   !Primes+ requires some memory as workspace, which dictates the maximum
   numbers the program can/will handle. The 'default' amount of allocated
   memory is set in the !Run file (see Primes$Memory), but this can be
   changed by the user to suit his/her requirements.
 
    You can add extra memory by clicking <Menu> on the !Primes icon.

    If you choose a number that is too big for the program to handle then
   it will abort. Run the !Primes+ program again and then immediately
   allocate some more memory by using <Menu>, as above.


  Notes on factorization:

   Largest integer computer can hold directly is 2,147,483,647 (=2^31-1)
   so this is the upper limit (for this program).

   Number of factors includes both 1 and the number itself -
   e.g 60 has 12 factors - viz. 1,2,3,4,5,6,10,12,15,20,30,60.

   Euler's function phi(N) is the number of integers in the set
   1,2,3,4,...,N-2,N-1 that are coprime to N (including 1 itself)
   e.g phi(12)=4 since 1,5,7,11 are coprime to 12.

   The number 1862340480 = 2^7*3^2*5*7*11*13*17*19 and the
   number 1745944200 = 2^3*3^3*5^2*7*11*13*17*19 both have 1536
   factors - and this seems to be the maximum for this machine.
   The number 2*3*5*7*11*13*17*19*23 = 223092870 has nine different
   prime factors, and is the maximum the machine can hold.

   Enjoy!

   Copyright :  R.A.Swetman
