The status as of 2010 is summarized in <A HREF="http://arxiv.org/abs/1010.1399">On a new property of primes that leads to a generalization of Cramer's conjecture</A> . (<A HREF="http://en.wikipedia.org/wiki/Firoozbakht%27s_conjecture">Firoozbakht's</A> conjecture is slightly stronger than <A HREF="http://en.wikipedia.org/wiki/Cramer%27s_conjecture">Cram&eacute;r's,</A> as explained <A HREF="http://www.primepuzzles.net/conjectures/conj_030.htm">here.</A>)

I find it noteworthy that <A HREF="http://www.primepuzzles.net/thepuzzlers/Firoozbakht.htm">Farideh Firoozbakht</A> proposed this conjecture (in 1982, not 1992) as an undergraduate student.