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Is it bad if Safari won't display/find my page at all?

I’ve edited my heading to try and get some opinions. Things are working OK on modern computers, BUT…

I have an older iMac ( a secondary computer) running Safari 6.8.2, which is the most recent version the OS (10.8.5) will run. I keep this to run some old software.

My website either won’t display or can’t be found at all, so I thought I may have done something wrong. It will however display fine on Chrome on the same system.

But yesterday I was looking to download the latest official Facebook print logos on the machine, and Safari wouldn’t load that page either. I got the message that it couldn’t establish a secure connection. I think I got this message for my page yesterday, but today it’s not finding it al all. It shows a search results page without my site on it. I think this MAY be because yesterday I had a google ads campaign running, but I paused it to fix some issues with my site.

So I’m unsure if this is something I even need to worry about. I just thought an old browser would still display something, even if it’s wrong…

thanks for any input.

the site is:

Here is my site Read-Only: LINK
(how to share your site Read-Only link)