Amaranth is a warm season plant and will mature to seed in about 100 days, so there is no need for most of us to start the seeds indoors early. Planting outside on Memorial Day or close to it will give you plenty of time for harvest. Greens can be harvested in just 3 weeks or so from planting.
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I like the idea of mixing the seeds with sand to get good spacing between plants. However, you can also use a seed disseminator to get the plants spaced evenly if you plant outside in rows.