7433 = (2 * 3716) + 1 ;
hence not 2 divides 7433 by NAT_4:9; :: thesis:
7433 = (3 * 2477) + 2 ;
hence not 3 divides 7433 by NAT_4:9; :: thesis:
7433 = (5 * 1486) + 3 ;
hence not 5 divides 7433 by NAT_4:9; :: thesis:
7433 = (7 * 1061) + 6 ;
hence not 7 divides 7433 by NAT_4:9; :: thesis:
7433 = (11 * 675) + 8 ;
hence not 11 divides 7433 by NAT_4:9; :: thesis:
7433 = (13 * 571) + 10 ;
hence not 13 divides 7433 by NAT_4:9; :: thesis:
7433 = (17 * 437) + 4 ;
hence not 17 divides 7433 by NAT_4:9; :: thesis:
7433 = (19 * 391) + 4 ;
hence not 19 divides 7433 by NAT_4:9; :: thesis:
7433 = (23 * 323) + 4 ;
hence not 23 divides 7433 by NAT_4:9; :: thesis:
7433 = (29 * 256) + 9 ;
hence not 29 divides 7433 by NAT_4:9; :: thesis:
7433 = (31 * 239) + 24 ;
hence not 31 divides 7433 by NAT_4:9; :: thesis:
7433 = (37 * 200) + 33 ;
hence not 37 divides 7433 by NAT_4:9; :: thesis:
7433 = (41 * 181) + 12 ;
hence not 41 divides 7433 by NAT_4:9; :: thesis:
7433 = (43 * 172) + 37 ;
hence not 43 divides 7433 by NAT_4:9; :: thesis:
7433 = (47 * 158) + 7 ;
hence not 47 divides 7433 by NAT_4:9; :: thesis:
7433 = (53 * 140) + 13 ;
hence not 53 divides 7433 by NAT_4:9; :: thesis:
7433 = (59 * 125) + 58 ;
hence not 59 divides 7433 by NAT_4:9; :: thesis:
7433 = (61 * 121) + 52 ;
hence not 61 divides 7433 by NAT_4:9; :: thesis:
7433 = (67 * 110) + 63 ;
hence not 67 divides 7433 by NAT_4:9; :: thesis:
7433 = (71 * 104) + 49 ;
hence not 71 divides 7433 by NAT_4:9; :: thesis:
7433 = (73 * 101) + 60 ;
hence not 73 divides 7433 by NAT_4:9; :: thesis:
7433 = (79 * 94) + 7 ;
hence not 79 divides 7433 by NAT_4:9; :: thesis:
7433 = (83 * 89) + 46 ;
hence not 83 divides 7433 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 7433 & n is prime holds
not n divides 7433 by XPRIMET1:46;
hence 7433 is prime by NAT_4:14; :: thesis: