is an interesting variant. Like Caroline mentioned, you won't have any success with this on properly formed RSA keys, but Hart's OLF will very quickly factor some poorly made ones, and works quite a bit better in that respect than standard Fermat. It not only quickly finds N=PQ where P=Q+x for a small x, but also where P=kQ+x for some integer k and small x. Again not something any proper RSA key generation method will produce, but the ways people can screw things up is pretty high, and it might be worth giving it a few seconds just in case.
For small values, unlike Hart I find SQUFOF to be faster, but this is implementation specific. HOLF is also, like Fermat's method, extremely simple to implement.
http://wrap.warwick.ac.uk/54707/1/WRAP_Hart_S144678871200014...
is an interesting variant. Like Caroline mentioned, you won't have any success with this on properly formed RSA keys, but Hart's OLF will very quickly factor some poorly made ones, and works quite a bit better in that respect than standard Fermat. It not only quickly finds N=PQ where P=Q+x for a small x, but also where P=kQ+x for some integer k and small x. Again not something any proper RSA key generation method will produce, but the ways people can screw things up is pretty high, and it might be worth giving it a few seconds just in case.
For small values, unlike Hart I find SQUFOF to be faster, but this is implementation specific. HOLF is also, like Fermat's method, extremely simple to implement.