To estimate a maximum purchase price for the coin in question, we can analyze the provided data, especially the hammer prices and starting prices from previous auctions, as well as the average hammer and starting prices.

1. Current starting price: 2000 euros.
2. Average starting price: 2791.51 euros.
3. Average hammer price: 3401.71 euros.
4. Hammer price history:
- Previous hammer prices varied significantly, with some reaching up to 8750 euros in recent auctions.
- Most hammer prices are between 2000 and 5000 euros, with some exceptional cases exceeding this figure.

5. Condition: No information is provided about the condition of this coin, which may affect its value. However, in previous auctions, coins with conditions between 90 and 100 have achieved higher hammer prices.

6. Trends: Observing previous auctions, it seems that coins of this reference tend to sell for above their starting price, especially when considering the higher hammer prices.

### Maximum Purchase Price Estimation:
Given that the average hammer price is 3401.71 euros and considering that the starting price is 2000 euros, a reasonable maximum purchase price could be positioned between the average hammer price and an additional percentage to reflect the possibility of competitive bidding.

Final estimation: A maximum purchase price could be approximately 4000 euros. This is based on the average hammer price and the trend that coins of this reference usually sell for above their starting price.