Twin primes

Definition. Twin primes are pairs $(p,p+2)$ with both prime.

List under $50$.
- $(3,5)$
- $(5,7)$
- $(11,13)$
- $(17,19)$
- $(29,31)$
- $(41,43)$

Conclusion. Six pairs with larger element $<50$.

Remark. The twin prime conjecture (infinitely many twin primes) remains open; the best known result (Zhang, 2013) shows infinitely many pairs with gap $\le 246$.