First of all, thank you all for your comments and advice.

As for the number of punctures I've had so far, they are 6-7 since I bought my Specialized Sirrus, that is to say in 4/5 months.
I must say that I've been using my bike almost every day, but I never ride in the country, just on city streets or roads.

It seems that Gatorskin are by far the most popular tires. As Air suggested, I'll have a closer look at the Vredestein Fortezza SE with the Slime liner, as well.

Thank you all!!