7333 = (2 * 3666) + 1 ;
hence not 2 divides 7333 by NAT_4:9; :: thesis:
7333 = (3 * 2444) + 1 ;
hence not 3 divides 7333 by NAT_4:9; :: thesis:
7333 = (5 * 1466) + 3 ;
hence not 5 divides 7333 by NAT_4:9; :: thesis:
7333 = (7 * 1047) + 4 ;
hence not 7 divides 7333 by NAT_4:9; :: thesis:
7333 = (11 * 666) + 7 ;
hence not 11 divides 7333 by NAT_4:9; :: thesis:
7333 = (13 * 564) + 1 ;
hence not 13 divides 7333 by NAT_4:9; :: thesis:
7333 = (17 * 431) + 6 ;
hence not 17 divides 7333 by NAT_4:9; :: thesis:
7333 = (19 * 385) + 18 ;
hence not 19 divides 7333 by NAT_4:9; :: thesis:
7333 = (23 * 318) + 19 ;
hence not 23 divides 7333 by NAT_4:9; :: thesis:
7333 = (29 * 252) + 25 ;
hence not 29 divides 7333 by NAT_4:9; :: thesis:
7333 = (31 * 236) + 17 ;
hence not 31 divides 7333 by NAT_4:9; :: thesis:
7333 = (37 * 198) + 7 ;
hence not 37 divides 7333 by NAT_4:9; :: thesis:
7333 = (41 * 178) + 35 ;
hence not 41 divides 7333 by NAT_4:9; :: thesis:
7333 = (43 * 170) + 23 ;
hence not 43 divides 7333 by NAT_4:9; :: thesis:
7333 = (47 * 156) + 1 ;
hence not 47 divides 7333 by NAT_4:9; :: thesis:
7333 = (53 * 138) + 19 ;
hence not 53 divides 7333 by NAT_4:9; :: thesis:
7333 = (59 * 124) + 17 ;
hence not 59 divides 7333 by NAT_4:9; :: thesis:
7333 = (61 * 120) + 13 ;
hence not 61 divides 7333 by NAT_4:9; :: thesis:
7333 = (67 * 109) + 30 ;
hence not 67 divides 7333 by NAT_4:9; :: thesis:
7333 = (71 * 103) + 20 ;
hence not 71 divides 7333 by NAT_4:9; :: thesis:
7333 = (73 * 100) + 33 ;
hence not 73 divides 7333 by NAT_4:9; :: thesis:
7333 = (79 * 92) + 65 ;
hence not 79 divides 7333 by NAT_4:9; :: thesis:
7333 = (83 * 88) + 29 ;
hence not 83 divides 7333 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 7333 & n is prime holds
not n divides 7333 by XPRIMET1:46;
hence 7333 is prime by NAT_4:14; :: thesis: