# [Jelly], 12 [bytes]

<sup>I'm not yet convinced this is as terse as possible.</sup>

    2‘×$⁸СÆfFQḣ

A monadic Link that accepts a positive integer, \$n\$, and yields a list of the first \$n\$ Sylvester primes.

**[Try it online!][TIO-m0nzhzzh]**

#### How?

    2‘×$⁸СÆfFQḣ - Link: positive integer, N
    2            - literal two (first value of Current, below)
         С      - collect, repeating...
        ⁸        - ...times: chain's left argument = N
       $         - ...action: last two links as a monad - f(Current):
     ‘           -              increment {Current} -> Current + 1
      ×          -              multiply {that] by {Current} -> Current × (Current + 1)
           Æf    - prime factors (vectorises)
             F   - flatten
              Q  - deduplicate
               ḣ - head {that} to index {N}


[Jelly]: https://github.com/DennisMitchell/jelly
[bytes]: https://github.com/DennisMitchell/jelly/wiki/Code-page

[TIO-m0nzhzzh]: https://tio.run/##ASEA3v9qZWxsef//MuKAmMOXJOKBuMOQwqHDhmZGUeG4o////zc "Jelly – Try It Online"