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

Yes

The spelling, meaning, and grammatical category of the word "prima" are identical in both Brazilian and Continental Portuguese. The primary difference lies in pronunciation. In Brazilian Portuguese, vowels are generally pronounced more openly and clearly. In Continental Portuguese, unstressed vowels are often "swallowed" or reduced (vowel reduction), making the word sound more closed or clipped. Additionally, while the word itself is the same, the grammatical patterns surrounding it—such as the use of definite articles before possessives—differ between the two regions.

Brazilian Portuguese Examples

1. Minha prima mora no Rio de Janeiro. (My cousin lives in Rio de/ Janeiro.)
2. Eu vou visitar minha prima amanhã. (I am going to visit my cousin tomorrow.)
3. Minha prima é muito legal. (My cousin is very cool.)
4. Você conhece minha prima? (Do you know my cousin?)
5. Minha prima me ligou ontem. (My cousin called me yesterday.)

Continental Portuguese Examples

1. A minha prima mora no Porto. (My cousin lives in Porto.)
2. Vou visitar a minha prima amanhã. (I am going to visit my cousin tomorrow.)
3. A minha prima é muito porreira. (My cousin is very cool.)
4. Conheces a minha prima? (Do you know my cousin?)
5. A minha prima ligou-me ontem. (My cousin called me yesterday.)