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Gold and platinum are 15-19 times heavier than other streambed materials and concentrate in low pressure areas and cracks that run across rivers and streams.
You look for a crack on the bank, and follow it out until you meet the "gold line" and there you suck it out with your dredge.
Gold will be on the outside edge of a river gravel bar, at the head of the bar (large gold but usually beneath big boulders), and at the tail end of a bar (vast concentrations due to river bars forming in the shape of an airfoil and sucking fine gold to the tail end) but be small to microscopic at the tail end.
Gold will travel down a river or stream in a line, usually off center of the high pressure water. Gold will settle behind a boulder.
A good place to fish, can also be an excellent place to find gold. "Black sand" is iron ore that can be readily identified in gravel bars and is a ready indicator that gold is probably present.
The most effective and economical way for the average person to find paying concentrations of gold in a river or stream is with a simple ($80) sluice that you shovel into and the riffles retain gold, platinum, gems and anything heavy for you.
Gold can be found up high on the old river channels and recovered with metal detectors, a gold wheel, a highbanker, or simply by identifying the material, shoveling it in your truck and working it out later in a wheel, or your simple stream sluice.
The states which have gold in vast quantities are: Maine, Vermont, Virginia, North Carolina, South Carolina, Georgia, Alabama, Colorado, Wyoming, New Mexico, Nevada, Arizona, California, Idaho, Washington, Montana, and Oregon.
The rest have gold as well, some in very good concentrations. All have gems of some kind that a sluice will separate and hold. Good luck finding the gold of your dreams!