To expand on this a little, 256-bit RSA is easily crackable, since there are good algorithms for integer factorization. You need a significant increase in key length to get equivalent security to symmetric keys: Wikipedia claims 3072-bit RSA ~ 128-bit symmetric, 15360-bit RSA ~ 256-bit symmetric. [0]

[0]: https://en.wikipedia.org/wiki/Key_size#Asymmetric_algorithm_...