Number 3 is a prime number, so are numbers 5 and 7; therefore it is clear that all odd numbers are prime numbers. Which fallacy is committed in the above argument?

The argument leaps from three odd primes to a sweeping claim about all odd numbers.

It notes that three, five and seven are prime numbers.

From these few cases it concludes that every odd number is prime.

A handful of instances cannot support a universal generalisation, and nine already breaks it.

Drawing a broad conclusion from too few cases is the fallacy of hasty generalisation.