How to define a list that contains all primes less than x?

Question

how can I define my own list in which I have all primes less than x?

Prime @ Range @ PrimePi @ x. See e.g. this question What is so special about Prime? to get an idea about possible limitations of this approach. — Artes, Commented May 7, 2014 at 17:21
Or Cases[Range@x, _?PrimeQ] But Artes version is much faster :) — Öskå, Commented May 7, 2014 at 17:25
@Öskå A possible alternative would be the NextPrime function see e.g. Why does iterating Prime in reverse order require much more time? for completing the method above. — Artes, Commented May 7, 2014 at 17:28
I would recommend also a closer look at this question Is there a way to use functions like Prime within Solve? — Artes, Commented May 7, 2014 at 17:57

2 revs · Accepted Answer · 2017-04-13 12:55:59Z

4

Prime @ Range @ PrimePi @ x. See e.g. this question What is so special about Prime? to get an idea about possible limitations of this approach.

Application of what is being said:

primeInf[x_] := Prime @ Range @ PrimePi @ x
primeInf@20

{2, 3, 5, 7, 11, 13, 17, 19}

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