Intermingled primes

Question

_{This puzzle is part of the Monthly Topic Challenge #14: Think inside the (very small) box!.}

6 different, 3 digit primes are stacked here in two layers.
You only see the sum of overlapping digits.

Find the 6 primes.

Answer 1

The 6 different primes are:

Row 1: 113
Row 2: 101
Row 3: 601
Column 1: 281
Column 2: 401
Column 3: 313

Deductions (I solved it with regular expressions in a list of all prime numbers from 101-997):

 -> Column 2:  /[1-5]01/           -> 101, 401

 -> Row 1:     /[12][14][0-5]/     -> 113, 211, 241

 -> Row 2      /[1-9]0[0-2]/       -> 101, 401, 601, 701

 -> Row 3:     /[1-7]0[0-4]/       -> 101, 103, 401, 503, 601, 701

 -> Column 3:  /[35]1[13]/         -> 311, 313

 -> Row 1:     /..3/               -> 113

 -> Column 2:  /4../               -> 401

 -> Row 2:     401                 -> 101, 601, 701

 -> Column 1:  /2[832][0-6]/       -> 223, 233, 281, 283

 -> Row 3      /^[46]/             -> 401, 601 -> 601

 -> Column 3:  /..3/               -> 313

 -> Row 2:     401, 601            -> 101, 701

 -> Column 1:  /..1/               -> 281

 -> Row 2:     /1../               -> 101