5981 = (2 * 2990) + 1 ;
hence not 2 divides 5981 by NAT_4:9; :: thesis:
5981 = (3 * 1993) + 2 ;
hence not 3 divides 5981 by NAT_4:9; :: thesis:
5981 = (5 * 1196) + 1 ;
hence not 5 divides 5981 by NAT_4:9; :: thesis:
5981 = (7 * 854) + 3 ;
hence not 7 divides 5981 by NAT_4:9; :: thesis:
5981 = (11 * 543) + 8 ;
hence not 11 divides 5981 by NAT_4:9; :: thesis:
5981 = (13 * 460) + 1 ;
hence not 13 divides 5981 by NAT_4:9; :: thesis:
5981 = (17 * 351) + 14 ;
hence not 17 divides 5981 by NAT_4:9; :: thesis:
5981 = (19 * 314) + 15 ;
hence not 19 divides 5981 by NAT_4:9; :: thesis:
5981 = (23 * 260) + 1 ;
hence not 23 divides 5981 by NAT_4:9; :: thesis:
5981 = (29 * 206) + 7 ;
hence not 29 divides 5981 by NAT_4:9; :: thesis:
5981 = (31 * 192) + 29 ;
hence not 31 divides 5981 by NAT_4:9; :: thesis:
5981 = (37 * 161) + 24 ;
hence not 37 divides 5981 by NAT_4:9; :: thesis:
5981 = (41 * 145) + 36 ;
hence not 41 divides 5981 by NAT_4:9; :: thesis:
5981 = (43 * 139) + 4 ;
hence not 43 divides 5981 by NAT_4:9; :: thesis:
5981 = (47 * 127) + 12 ;
hence not 47 divides 5981 by NAT_4:9; :: thesis:
5981 = (53 * 112) + 45 ;
hence not 53 divides 5981 by NAT_4:9; :: thesis:
5981 = (59 * 101) + 22 ;
hence not 59 divides 5981 by NAT_4:9; :: thesis:
5981 = (61 * 98) + 3 ;
hence not 61 divides 5981 by NAT_4:9; :: thesis:
5981 = (67 * 89) + 18 ;
hence not 67 divides 5981 by NAT_4:9; :: thesis:
5981 = (71 * 84) + 17 ;
hence not 71 divides 5981 by NAT_4:9; :: thesis:
5981 = (73 * 81) + 68 ;
hence not 73 divides 5981 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5981 & n is prime holds
not n divides 5981 by XPRIMET1:42;
hence 5981 is prime by NAT_4:14; :: thesis: