Is this coin biased?

A coin is flipped 1,000 times and shows 530 heads.

(a) Test $H_0: p = 0.5$ against a two-sided alternative at $\alpha = 0.05$. What is the p-value?

(b) Give a 95% confidence interval for $p$.

(c) If the heads rate stayed at 53%, roughly how many flips would you need before the result became significant at 5% (two-sided)?