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Every Mott number is divisible by 6 because 2 and 3 must be two of the factors.
The smallest product of 5 primes without both 2 and 3 is 2 * 5 * 7 * 11 * 13 = 10010. This is a 5-digit number and thus, by definition, cannot be a Mott number.
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What four digit number are divisible by 3 and 6?
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every thing is divisible by 6
