2 added 285 characters in body
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Pyth, 1110 bytes

*Q*FfP_TStQ*Q*FfP_TSt

Explanation incoming! I'm pretty sure this can be golfed some more, too...


*Q*FfP_TSt     Full program, takes input from stdin and outputs to stdout
*Q             Implicitly output $input multiplied by 
  *F           The product of
        St(Q)  All numbers less than $input (Q is added automtaically by Pyth)
    fP_T       As long as they are prime

Pyth, 11 bytes

*Q*FfP_TStQ

Explanation incoming! I'm pretty sure this can be golfed some more, too.

Pyth, 10 bytes

*Q*FfP_TSt

I'm pretty sure this can be golfed some more...


*Q*FfP_TSt     Full program, takes input from stdin and outputs to stdout
*Q             Implicitly output $input multiplied by 
  *F           The product of
        St(Q)  All numbers less than $input (Q is added automtaically by Pyth)
    fP_T       As long as they are prime
1
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Pyth, 11 bytes

*Q*FfP_TStQ

Explanation incoming! I'm pretty sure this can be golfed some more, too.