Task

Write a program which counts up from   1,   displaying each number as the multiplication of its prime factors.

For the purpose of this task,   1   (unity)   may be shown as itself.



Example

      2   is prime,   so it would be shown as itself.

      6   is not prime;   it would be shown as   



2
×
3


{\displaystyle 2\times 3}

.
2144   is not prime;   it would be shown as   



2
×
2
×
2
×
2
×
2
×
67


{\displaystyle 2\times 2\times 2\times 2\times 2\times 67}

.



Related tasks

   prime decomposition
   factors of an integer
   Sieve of Eratosthenes
   primality by trial division
   factors of a Mersenne number
   trial factoring of a Mersenne number
   partition an integer X into N primes


for i = 1000 to 1016
  print i;" = "; factorial$(i)
next
wait
function factorial$(num)
 if num = 1 then factorial$ = "1"
 fct = 2
 while fct <= num
 if (num mod fct) = 0 then
   factorial$ = factorial$ ; x$ ; fct
   x$  = " x "
   num = num / fct
  else
   fct = fct + 1
 end if
 wend
end function