8807 = (2 * 4403) + 1 ;
hence not 2 divides 8807 by NAT_4:9; :: thesis:
8807 = (3 * 2935) + 2 ;
hence not 3 divides 8807 by NAT_4:9; :: thesis:
8807 = (5 * 1761) + 2 ;
hence not 5 divides 8807 by NAT_4:9; :: thesis:
8807 = (7 * 1258) + 1 ;
hence not 7 divides 8807 by NAT_4:9; :: thesis:
8807 = (11 * 800) + 7 ;
hence not 11 divides 8807 by NAT_4:9; :: thesis:
8807 = (13 * 677) + 6 ;
hence not 13 divides 8807 by NAT_4:9; :: thesis:
8807 = (17 * 518) + 1 ;
hence not 17 divides 8807 by NAT_4:9; :: thesis:
8807 = (19 * 463) + 10 ;
hence not 19 divides 8807 by NAT_4:9; :: thesis:
8807 = (23 * 382) + 21 ;
hence not 23 divides 8807 by NAT_4:9; :: thesis:
8807 = (29 * 303) + 20 ;
hence not 29 divides 8807 by NAT_4:9; :: thesis:
8807 = (31 * 284) + 3 ;
hence not 31 divides 8807 by NAT_4:9; :: thesis:
8807 = (37 * 238) + 1 ;
hence not 37 divides 8807 by NAT_4:9; :: thesis:
8807 = (41 * 214) + 33 ;
hence not 41 divides 8807 by NAT_4:9; :: thesis:
8807 = (43 * 204) + 35 ;
hence not 43 divides 8807 by NAT_4:9; :: thesis:
8807 = (47 * 187) + 18 ;
hence not 47 divides 8807 by NAT_4:9; :: thesis:
8807 = (53 * 166) + 9 ;
hence not 53 divides 8807 by NAT_4:9; :: thesis:
8807 = (59 * 149) + 16 ;
hence not 59 divides 8807 by NAT_4:9; :: thesis:
8807 = (61 * 144) + 23 ;
hence not 61 divides 8807 by NAT_4:9; :: thesis:
8807 = (67 * 131) + 30 ;
hence not 67 divides 8807 by NAT_4:9; :: thesis:
8807 = (71 * 124) + 3 ;
hence not 71 divides 8807 by NAT_4:9; :: thesis:
8807 = (73 * 120) + 47 ;
hence not 73 divides 8807 by NAT_4:9; :: thesis:
8807 = (79 * 111) + 38 ;
hence not 79 divides 8807 by NAT_4:9; :: thesis:
8807 = (83 * 106) + 9 ;
hence not 83 divides 8807 by NAT_4:9; :: thesis:
8807 = (89 * 98) + 85 ;
hence not 89 divides 8807 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 8807 & n is prime holds
not n divides 8807 by XPRIMET1:48;
hence 8807 is prime by NAT_4:14; :: thesis: