Chrome and Safari on OS X and IOS can’t open SSL-secured sites with keysizes greater 4096 bit. As mentioned by Samuel Tardieu it’s a apple fail. I can’t think of a good reason why more bits are a security problem.
This works great except for Apple-User.
Certificate: Data: Version: 3 (0x2) Serial Number: 144413 (0x2341d) Signature Algorithm: sha512WithRSAEncryption Issuer: O=CAcert Inc., OU=http://www.CAcert.org, CN=CAcert Class 3 Root Validity Not Before: Apr 28 07:05:30 2014 GMT Not After : Apr 27 07:05:30 2016 GMT Subject: CN= migmedia.net Subject Public Key Info: Public Key Algorithm: rsaEncryption Public-Key: (8192 bit) Modulus: