The minimum number is 13.
If we share as many coins as possible, we would end up at 102 coins, if we give the coins to 12 persons:
3, 4, 5,6 , 7, 8, 9, 10, 11, 12, 13, 14
Unfortunatly its not possible to reach 99 with 12 persons – only 100 or 98 is possible. So we need more persons.
With 13 it works:
3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 11, 12, 13