Factor This 10-Digit Number

The number \( 1003003001\) is the product of \(N\) (not necessarily distinct) primes. What is the value of \(N\)?

Details and assumptions:

  • The number \( 32 = 2\times 2 \times 2 \times 2 \times 2 \) is the product of 5 primes.
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