If you allow 3 x 3 x 3 x 3, then 81.
If they must be different then 1155.
23 x 53 = 1000
Logically, the smallest number with 4 different prime factors would have to be the product of the smallest four prime numbers. So the smallest natural number with four different prime factors is 210 (2*3*5*7).
1155, 3x5x7x11=1155.
2×3×5×7=210
1009
The smallest number divisible by first four prime numbers is 2x3x5x7 = 210.
The four smallest prime numbers are 2, 3, 5, and 7. Their product is 2 x 3 x 5 x 7 = 210. Thus, the smallest number that is divisible by four different prime numbers is 210.
No prime number can be divided by 4 exactly.
210
1155
You had me until "product." The product of 4 digits can't be prime.
The smallest four prime numbers are 2, 3, 5, 7, and their sum happens to be a prime.