[FiloSottile]

> Rule of thumb: Want a 1024-bit prime? Try 1024 1024-bit candidates and you'll probably find one.

Where probably is 76% [1], which is not that high depending on what you are doing. For example, you wouldn't be ok with GenerateKey failing 24% of the time.

To get a better than even chance, 491 [2] 1024-bit candidates are enough.

[1]: https://www.wolframalpha.com/input?i=1+-+%281+-+li%282%5E102... (using li(x) as a slightly better approximation of π(x) than x/ln(x), see [3])

[2]: https://www.wolframalpha.com/input?i=1+-+%281+-+li%282%5E102...

[3]: https://en.wikipedia.org/wiki/Prime-counting_function