We call a natural number $p{}$ [i]simple[/i] if for any natural number $k{}$ such that $2\leqslant k\leqslant \sqrt{p}$ the inequality $\{p/k\}\geqslant 0,01$ holds. Is the set of simple prime numbers finite?

[i]Proposed by M. Didin[/i]
1. **Understanding the Problem:**
   We need to determine if the set of simple prime numbers is finite. A prime number \( p \) is called *simple* if for any natural number \( k \) such that \( 2 \leq k \leq \sqrt{p} \), the inequality \( \{p/k\} \geq 0.01 \) holds, where \( \{x\} \) denotes the fractional part of \( x \).

2. **Analyzing the Condition:**
   The fractional part \( \{p/k\} \) is given by:
   \[
   \{p/k\} = p/k - \left\lfloor p/k \right\rfloor
   \]
   For \( p \) to be simple, we need:
   \[
   p/k - \left\lfloor p/k \right\rfloor \geq 0.01
   \]
   for all \( k \) in the range \( 2 \leq k \leq \sqrt{p} \).

3. **Choosing \( k \):**
   Consider \( k = \left\lfloor \sqrt{p} \right\rfloor \). For large \( p \), \( k \) is approximately \( \sqrt{p} \). We need to check if:
   \[
   \left\{ \frac{p}{\left\lfloor \sqrt{p} \right\rfloor} \right\} \geq 0.01
   \]

4. **Bounding \( p \):**
   Let \( n = \left\lfloor \sqrt{p} \right\rfloor \). Then:
   \[
   n^2 \leq p < (n+1)^2
   \]
   This implies:
   \[
   \frac{p}{n} \approx n \quad \text{and} \quad \frac{p}{n+1} \approx n
   \]

5. **Fractional Part Analysis:**
   For \( p \) to be simple, we need:
   \[
   \left\{ \frac{p}{n} \right\} \geq 0.01
   \]
   and similarly for other \( k \) values in the range. If \( p \) is very large, the fractional part \( \left\{ \frac{p}{n} \right\} \) can be very small, potentially less than 0.01.

6. **Conclusion:**
   As \( p \) increases, the fractional part \( \left\{ \frac{p}{k} \right\} \) for some \( k \) in the range \( 2 \leq k \leq \sqrt{p} \) can become arbitrarily small. Therefore, there exists a sufficiently large prime \( p \) such that \( \left\{ \frac{p}{k} \right\} < 0.01 \) for some \( k \). This implies that not all large primes can be simple.

\[
\boxed{\text{The set of simple prime numbers is finite.}}
\]