9803 = (2 * 4901) + 1 ;
hence not 2 divides 9803 by NAT_4:9; :: thesis:
9803 = (3 * 3267) + 2 ;
hence not 3 divides 9803 by NAT_4:9; :: thesis:
9803 = (5 * 1960) + 3 ;
hence not 5 divides 9803 by NAT_4:9; :: thesis:
9803 = (7 * 1400) + 3 ;
hence not 7 divides 9803 by NAT_4:9; :: thesis:
9803 = (11 * 891) + 2 ;
hence not 11 divides 9803 by NAT_4:9; :: thesis:
9803 = (13 * 754) + 1 ;
hence not 13 divides 9803 by NAT_4:9; :: thesis:
9803 = (17 * 576) + 11 ;
hence not 17 divides 9803 by NAT_4:9; :: thesis:
9803 = (19 * 515) + 18 ;
hence not 19 divides 9803 by NAT_4:9; :: thesis:
9803 = (23 * 426) + 5 ;
hence not 23 divides 9803 by NAT_4:9; :: thesis:
9803 = (29 * 338) + 1 ;
hence not 29 divides 9803 by NAT_4:9; :: thesis:
9803 = (31 * 316) + 7 ;
hence not 31 divides 9803 by NAT_4:9; :: thesis:
9803 = (37 * 264) + 35 ;
hence not 37 divides 9803 by NAT_4:9; :: thesis:
9803 = (41 * 239) + 4 ;
hence not 41 divides 9803 by NAT_4:9; :: thesis:
9803 = (43 * 227) + 42 ;
hence not 43 divides 9803 by NAT_4:9; :: thesis:
9803 = (47 * 208) + 27 ;
hence not 47 divides 9803 by NAT_4:9; :: thesis:
9803 = (53 * 184) + 51 ;
hence not 53 divides 9803 by NAT_4:9; :: thesis:
9803 = (59 * 166) + 9 ;
hence not 59 divides 9803 by NAT_4:9; :: thesis:
9803 = (61 * 160) + 43 ;
hence not 61 divides 9803 by NAT_4:9; :: thesis:
9803 = (67 * 146) + 21 ;
hence not 67 divides 9803 by NAT_4:9; :: thesis:
9803 = (71 * 138) + 5 ;
hence not 71 divides 9803 by NAT_4:9; :: thesis:
9803 = (73 * 134) + 21 ;
hence not 73 divides 9803 by NAT_4:9; :: thesis:
9803 = (79 * 124) + 7 ;
hence not 79 divides 9803 by NAT_4:9; :: thesis:
9803 = (83 * 118) + 9 ;
hence not 83 divides 9803 by NAT_4:9; :: thesis:
9803 = (89 * 110) + 13 ;
hence not 89 divides 9803 by NAT_4:9; :: thesis:
9803 = (97 * 101) + 6 ;
hence not 97 divides 9803 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9803 & n is prime holds
not n divides 9803 by XPRIMET1:50;
hence 9803 is prime by NAT_4:14; :: thesis: