This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.
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Springer
T. Rabin
Pushing the factoring boundary to 768 bits
IACR Crypto
Cryptology

Kleinjung, T., Aoki, K., Franke, J., Lenstra, A., Thomee, E., Bos, J., … Zimmermann, P. (2010). Factorization of a 768-bit RSA modulus. In T. Rabin (Ed.), Proceedings of Advances in Cryptology - CRYPTO 2010 2010 (pp. 333–350). Springer.