BRUSSELS, Dec 2 (Reuters) - Euro zone producer prices jumped more than expected in October, data showed on Thursday, driven mainly by a surge in energy prices, while unemployment eased again as the economy continued to recover from the pandemic-induced recession. The European Union"s statistics office Eurostat said prices at factory gates in the 19 countries sharing the euro rose 5.4% month-on-month for a 21.9% year-on-year surge.Economists polled by Reuters had expected a 3.5% monthly rise and a 19.0% annual gain. Energy prices were the main reason behind the sharp increase, surging 16.8% on the month and rocketing 62.5% year-on-year. Producer prices translate into higher prices for consumers and in November headline consumer inflation reached 4.9%, by far the highest level in the 25 years since the figure has been compiled, up from 4.1% a month earlier and well ahead of expectations for 4.5%.Eurostat said the euro zone jobless rate continued to decline, falling to 7.3% of the workforce in October, as expected by economists polled by Reuters, from 7.4% in September. Eurostat said the number of people without jobs fell to 12.045 million in October from 12.109 in September.