You need to be very careful when you apply for naturalization because USCIS might revoke your Permanent Residency and would place you on a deportation proceeding as a result of breaking of your marriage within a few months of obtaining full GC. I was an aggressive Immigration attorney and know so many cases wherein USCIS has done this. At the time of naturalization, applicants WHOLE IMMIGRATION JOURNEY is scrutnized. You might say that you were genuinely married to your spouse for 3 or more years but whenever a marriage breaks down within a few months of obtaining GC then it's an automatic presumption of USCIS that there might be a possible immigration fraud.
When I said earlier that applicants are also required to be happily married until oath is taken for naturalization purpose then I was meant that USCIS shouldn't know that marriage is getting rocky/shaky or on the verge of breaking it up; otherwise they would definately deny the application under that ground. Just being legally married alone is not enough, unless USCIS won't know about the shaky marriage. The ground of allowing applicants to file N-400 after being a GC for 3 yrs if they are still married and living to a US citizen is ONLY for the benefit of US citizen. So if an applicant is not legally married or not living happily with a US citizen then such applicant cannot file N-400 under this ground. Period.
In your case, even waiting for many years for Naturalization won't keep you out of the hook because the fact would still remain the same that your marriage fell apart shortly after obtaining GC. Thus, it's VERY important for you to collect as many documentary evidences as possible about the bonafide of your marriage."