Vyxal, 18 16 13 bytes

Thanks to The Thonnu for -5 bytes

£ƛ¥$%¬$æ∧;∑1=

Run it

Explanation:

£             # save to register
 ƛ       ;    # map over it with this code:
  ¥           # retrieve from register
   $          # swap
    %         # modulo
     ¬        # logical not
      $       # swap
       æ      # is the item prime?
        ∧     # logical and

          ∑   # sum
           1= # is 1?

Vyxal, 18 16 13 11 bytes

Thanks to The Thonnu for -7 bytes

ƛ?$Ḋ$æ∧;∑1=

Run it

Explanation:

ƛ      ;    # map over the input with this code:
 ?          # get input
  $         # swap
   Ḋ        # divisible?
    $       # swap
     æ      # is the item prime?
      ∧     # logical and

        ∑   # sum
         1= # is 1?

Vyxal, 18 16 bytes

Thanks to The Thonnu for -2 bytes

:£ɾƛ:¥$%¬$æ∧;∑1=

Run it

Explanation:

:                # duplicate the input
 £               # save to register
  ɾ              # get the inclusive range starting from 1
   ƛ        ;    # map over it with this code:
    :            # duplicate the item
     ¥           # retrieve from register
      $          # swap
       %         # modulo
        ¬        # logical not
         $       # swap
          æ      # is the item prime?
           ∧     # logical and

             ∑   # sum
              1= # is 1

Vyxal, 18 16 13 bytes

Thanks to The Thonnu for -5 bytes

£ƛ¥$%¬$æ∧;∑1=

Run it

Explanation:

£             # save to register
 ƛ       ;    # map over it with this code:
  ¥           # retrieve from register
   $          # swap
    %         # modulo
     ¬        # logical not
      $       # swap
       æ      # is the item prime?
        ∧     # logical and

          ∑   # sum
           1= # is 1?

Vyxal, 18 bytes

:→xɾƛ:←x$%¬$æ∧;∑1=

Run it

Explanation:

:                  # duplicate the input
 →x                # assign it to x
   ɾ               # get the inclusive range starting from 1
    ƛ         ;    # map over it with this code:
     :             # duplicate the item
      ←x           # retrieve x
        $          # swap
         %         # modulo
          ¬        # logical not
           $       # swap
            æ      # is the item prime?
             ∧     # logical and

               ∑   # sum
                1= # is 1

Vyxal, 18 16 bytes

Thanks to The Thonnu for -2 bytes

:£ɾƛ:¥$%¬$æ∧;∑1=

Run it

Explanation:

:                # duplicate the input
 £               # save to register
  ɾ              # get the inclusive range starting from 1
   ƛ        ;    # map over it with this code:
    :            # duplicate the item
     ¥           # retrieve from register
      $          # swap
       %         # modulo
        ¬        # logical not
         $       # swap
          æ      # is the item prime?
           ∧     # logical and

             ∑   # sum
              1= # is 1