If the product of 1000 natural numbers is 1000, then what is their minimum sum?

1000
1015
1027
1031

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1000 = 5 x 5 x 5 x 2 x 2 x 2 = 5 x 5 x 5 x 2 x 2 x 2 x 1 x 1 x 1 x ..... 994 1's

So their minimum sum is 5x3 + 2x3 + 1x994 = 1015