Calculation of 2 to the power 17398 modulo 17399



    keep squaring and reducing modulo   | keep dividing
         17399 as needed                | by two, dropping
----------------------------------------| remainder, but
                    square | square mod | marking odd expo-
                           | 17399      | nents where remainder
                                        | was dropped
---------------------------------------------------------------
                                    2   |  17398
                                        |
                         4          4   |   8699  *
                                        |
                        16         16   |   4349  *
                                        |
                       256        256   |   2174
                                        | 
                     65536      13339   |   1087  *
                                        |  
                 177928921       6747   |    543  *
                                        |  
                  45522009       6225   |    271  *
                                        | 
                  38750625       3052   |    135  *
                                        | 
                   9314704       6239   |     67  *
                                        | 
                  38925121       3558   |     33  *
                                        | 
                  12659364      10291   |     16
                                        |
                 105904681      14367   |      8
                                        |
                 206410689       6352   |      4
                                        | 
                  40347904      17022   |      2
                                        | 
                 289748484       2937   |      1  *
                                        | 
                  8625969       13464   |      0
 

What does the table mean, written out?

  17398             8699                  8699                       2174
 2      congruent  4      congruent 4 * 16     congruent 4 * 16 * 256 

                         1087                                   543 
congruent  4 * 16 * 13339      congruent   4 * 16 * 13339 * 6747    etc


... congruent 4 * 16 * 13339 * 6747 * 6225 * 3052 * 6239 * 3558 * 2937

congruent 16518