All numbers ≤4 divide 10 (the base of the numeral system of this wiki), but 5 does not. (note that 10 is the smallest such number)

All numbers ≤4 satisfy the property that general polynomial equation of degree n has a solution in radicals, but 5 does not. (all numbers ≥5 do not)

All numbers ≤4 satisfy the property that the Fermat number 2^(2^n)+1 is prime, but 5 does not. (all numbers from 5 to 28 do not)

All numbers ≤4 satisfy the property that the double Mersenne number 2^(2^(nth prime)−1)−1 is prime, but 5 does not. (all numbers from 5 to 15 do not)

All numbers ≤4 satisfy the property that the completed graph K_n is planar graph, but 5 does not. (all numbers ≥5 do not)

All numbers ≤4 satisfy the property that 1/n has terminated dozenal, but 5 does not. (only the 3-smooth numbers do)

All numbers ≤4 satisfy the property that the alternating group A_n is a solvable group, but 5 does not. (all numbers ≥5 do not)

All numbers ≤4 satisfy the property that the Lucas number L(2^n) is prime, but 5 does not. (all numbers from 5 to 20 do not)

10 (the base of the numeral system of this wiki) is the least common multiple of the numbers ≤4. (note that this is true only for “the set of the numbers ≤4”, this is true neither for “the set of the numbers ≤3” nor for “the set of the numbers ≤5”)

The Number 4! is 20, is has a lot of it's own properties

 v • e Donzenal Numbers 0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - X - E - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 1X - 1E - 20 - 26 - 32 - 34 - 42 - 50 - 5X - 68 - 76 - 84 - 85 - 100 - 111 - 148 - 375 - 3XE - 5E6 - 666 - 6E4 - 771 - 920 - 1001 - 2047 - 2497 - 2E00 - 186X35