Is the word primos the same in Brazilian and European Portuguese?

Yes

The word "primos" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are typically more open and the unstressed "o" is clearly articulated (sounding like a closed "o" or a very light "u"). In Continental Portuguese, unstressed vowels are much more reduced; therefore, the "o" in "primos" sounds much more like a short, whispered "u" ([ˈpɾimus]).

Brazilian Portuguese Examples

1. Meus primos vão chegar logo. (My cousins are going to arrive soon.)
2. Eu adoro brincar com meus primos. (I love playing with my cousins.)
3. Meus primos moram perto da minha casa. (My cousins live near my house.)
4. Você viu meus primos na festa? (Did you see my cousins at the party?)
5. Meus primos são muito legais. (My cousins are very cool.)

Continental Portuguese Examples

1. Os meus primos vão chegar já. (My cousins are arriving shortly.)
2. Eu adoro brincar com os meus primos. (I love playing with my cousins.)
3. Os meus primos moram perto da minha casa. (My cousins live near my house.)
4. Viste os meus primos na festa? (Did you see my cousins at the party?)
5. Os meus primos são muito fixes. (My cousins are very cool.)