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Instructions

The aim of the kata is to decompose n! (factorial n) into its prime factors.

Examples:

n = 12; decomp(12) -> "2^10 * 3^5 * 5^2 * 7 * 11"
since 12! is divisible by 2 ten times, by 3 five times, by 5 two times and by 7 and 11 only once.

n = 22; decomp(22) -> "2^19 * 3^9 * 5^4 * 7^3 * 11^2 * 13 * 17 * 19"

n = 25; decomp(25) -> 2^22 * 3^10 * 5^6 * 7^3 * 11^2 * 13 * 17 * 19 * 23

Prime numbers should be in increasing order. When the exponent of a prime is 1 don't put the exponent.

Notes

  • The function is decomp(n) and should return the decomposition of n! into its prime factors in increasing order of the primes, as a string.
  • Factorial can be a very big number (4000! has 12674 digits, n will go from 300 to 4000).
  • In Fortran - as in any other language - the returned string is not permitted to contain any redundant trailing whitespace: you can use dynamically allocated character strings.