Introduction:
Prime numbers are the numbers that can only be divided by 1 and itself. The form 10n+3 is a specific form of prime numbers where n is a whole number. In this question, we need to find out the number of prime numbers of this form.

Method:
To find the number of prime numbers of the form 10n+3, we need to use a specific theorem called Dirichlet's theorem. According to this theorem, if a and b are coprime positive integers, then there are infinitely many primes of the form a+bn, where n is a non-negative integer.

Application of Dirichlet's theorem:
We can apply Dirichlet's theorem to find the number of prime numbers of the form 10n+3. For this, we need to take a=3 and b=10. As 3 and 10 are coprime, Dirichlet's theorem implies that there are infinitely many primes of the form 10n+3.

Examples:
To verify this, let's take a few examples of n and check if 10n+3 is a prime number or not.

When n=1, 10n+3=13 (prime)
When n=2, 10n+3=23 (prime)
When n=3, 10n+3=33 (not prime)
When n=4, 10n+3=43 (prime)
When n=5, 10n+3=53 (prime)

Conclusion:
From the above examples, we can see that not all the numbers of the form 10n+3 are prime, but there are infinitely many primes of this form. Therefore, we cannot determine the exact number of prime numbers of the form 10n+3.