The very sane opening paragraph is:

On December 12, 2009, we factored the 768-bit, 232-digit number RSA-768 by the number field sieve (NFS, [19]). The number RSA-768 was taken from the now obsolete RSA Challenge list [37] as a representative 768-bit RSA modulus (cf. [36]). This result is a record for factoring general integers. Factoring a 1024-bit RSA modulus would be about a thousand times harder, and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one. Because the first factorization of a 512-bit RSA modulus was reported only a decade ago (cf. [7]) it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours or the one in [7]. Thus, it would be prudent to phase out usage of 1024-bit RSA within the next three to four years.

It’s an interesting read if factoring fascinates you.