9337 = (2 * 4668) + 1 ;
hence not 2 divides 9337 by NAT_4:9; :: thesis:
9337 = (3 * 3112) + 1 ;
hence not 3 divides 9337 by NAT_4:9; :: thesis:
9337 = (5 * 1867) + 2 ;
hence not 5 divides 9337 by NAT_4:9; :: thesis:
9337 = (7 * 1333) + 6 ;
hence not 7 divides 9337 by NAT_4:9; :: thesis:
9337 = (11 * 848) + 9 ;
hence not 11 divides 9337 by NAT_4:9; :: thesis:
9337 = (13 * 718) + 3 ;
hence not 13 divides 9337 by NAT_4:9; :: thesis:
9337 = (17 * 549) + 4 ;
hence not 17 divides 9337 by NAT_4:9; :: thesis:
9337 = (19 * 491) + 8 ;
hence not 19 divides 9337 by NAT_4:9; :: thesis:
9337 = (23 * 405) + 22 ;
hence not 23 divides 9337 by NAT_4:9; :: thesis:
9337 = (29 * 321) + 28 ;
hence not 29 divides 9337 by NAT_4:9; :: thesis:
9337 = (31 * 301) + 6 ;
hence not 31 divides 9337 by NAT_4:9; :: thesis:
9337 = (37 * 252) + 13 ;
hence not 37 divides 9337 by NAT_4:9; :: thesis:
9337 = (41 * 227) + 30 ;
hence not 41 divides 9337 by NAT_4:9; :: thesis:
9337 = (43 * 217) + 6 ;
hence not 43 divides 9337 by NAT_4:9; :: thesis:
9337 = (47 * 198) + 31 ;
hence not 47 divides 9337 by NAT_4:9; :: thesis:
9337 = (53 * 176) + 9 ;
hence not 53 divides 9337 by NAT_4:9; :: thesis:
9337 = (59 * 158) + 15 ;
hence not 59 divides 9337 by NAT_4:9; :: thesis:
9337 = (61 * 153) + 4 ;
hence not 61 divides 9337 by NAT_4:9; :: thesis:
9337 = (67 * 139) + 24 ;
hence not 67 divides 9337 by NAT_4:9; :: thesis:
9337 = (71 * 131) + 36 ;
hence not 71 divides 9337 by NAT_4:9; :: thesis:
9337 = (73 * 127) + 66 ;
hence not 73 divides 9337 by NAT_4:9; :: thesis:
9337 = (79 * 118) + 15 ;
hence not 79 divides 9337 by NAT_4:9; :: thesis:
9337 = (83 * 112) + 41 ;
hence not 83 divides 9337 by NAT_4:9; :: thesis:
9337 = (89 * 104) + 81 ;
hence not 89 divides 9337 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9337 & n is prime holds
not n divides 9337 by XPRIMET1:48;
hence 9337 is prime by NAT_4:14; :: thesis: