Parsnips are one of those seeds where the latter certainly applies and use of old seed is not recommended. We had sown a tray with seed from old opened packets (one and two years old). Nothing was seen of them again. Another tray was sown with fresh seed from a new packet and three weeks later they're pretty much all up. That first tray was reused and had the fresh seed sown about a week after the first and they're now showing their heads above the soil level.
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Now then I'd better get digging down the plot to get a couple of beds for roots to go in - these and the carrots will be ready to go out in no time I'm sure.