# [Jelly], 13 [bytes]

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

    2‘×$⁸СÆfZFQḣ

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‘×$⁸СÆfZFQḣ - 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)
             Z    - transpose
              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/##ASIA3f9qZWxsef//MuKAmMOXJOKBuMOQwqHDhmZaRlHhuKP///83 "Jelly – Try It Online"