How to determine the primary Uniprot accession number from a list of accession numbers?
I think there is an issue with the terminology. The "primary" accession number, is the first accession number in cases where an entry has more than one accession number, as described in http://www.uniprot.org/help/accession_numbers:


  Entries can have more than one accession number. This can be due to
  two distinct mechanisms:

a) When two or more entries are merged, the accession numbers from all entries are kept. The first accession number is referred to as the

  
  ‘Primary (citable) accession number’, while the others are referred to
  as ‘Secondary accession numbers’. These are listed in alphanumerical
  order.

b) If an existing entry is split into two or more entries (‘demerged’), new ‘primary’ accession numbers are attributed to all

  
  the split entries while all original accession numbers are retained as
  ‘secondary’ accession numbers.
  
  Example: P29358 which has been ‘demerged’ into P68250 and P68251.


Both reviewed and unreviewed entries can have primary accession numbers.

What you probably mean, as previous posters understood, are accession numbers of reviewed entries as opposed to unreviewed ones.

In that case, you can indeed add "reviewed:yes" to your query, e.g. when you are using the UniProt ID mapping, http://www.uniprot.org/help/uploadlists