Microsoft Internet Explorer usually has the fastest startup time on Microsoft Windows machines, although this is mostly because the real "price" of starting it up is paid during the booting of your Microsoft Windows system, whether you really want it or not. Beginning with version 7, Internet Explorer also features tabbed browsing, a feature that began life in Firefox. Tabbed browsing speeds up the process of dealing with many open web pages at once.
Opera is the fastest browser in terms of placing minimal demands on an older computer. Since Opera is written in well-optimized machine language, nothing else comes close to its sheer performance, especially on an old computer. Opera is free, so give it a try.
Firefox is a very fast descendant of Mozilla, well-tuned for real-world browsing experiences, with an interface that speeds up the way you get things done in a web browser by offering features like tabbed browsing and a more elegant "find" feature -- another relevant kind of speed. Firefox also offers good startup performance and excellent page layout performance.
Apple's Safari browser, seen on MacOS X systems, is derived from KDE's Konqueror browser, most frequently seen on Linux systems. Both of these browsers offer good startup performance and tabbed browsing, but somewhat clunky user interfaces when compared to Firefox.
Of course, no web browser can make a slow modem work faster. If what you really want is to download large files more quickly, your choice of web browser is not an important consideration. For more information, see why is my modem so slow?
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