5281 = (2 * 2640) + 1 ;
hence not 2 divides 5281 by NAT_4:9; :: thesis:
5281 = (3 * 1760) + 1 ;
hence not 3 divides 5281 by NAT_4:9; :: thesis:
5281 = (5 * 1056) + 1 ;
hence not 5 divides 5281 by NAT_4:9; :: thesis:
5281 = (7 * 754) + 3 ;
hence not 7 divides 5281 by NAT_4:9; :: thesis:
5281 = (11 * 480) + 1 ;
hence not 11 divides 5281 by NAT_4:9; :: thesis:
5281 = (13 * 406) + 3 ;
hence not 13 divides 5281 by NAT_4:9; :: thesis:
5281 = (17 * 310) + 11 ;
hence not 17 divides 5281 by NAT_4:9; :: thesis:
5281 = (19 * 277) + 18 ;
hence not 19 divides 5281 by NAT_4:9; :: thesis:
5281 = (23 * 229) + 14 ;
hence not 23 divides 5281 by NAT_4:9; :: thesis:
5281 = (29 * 182) + 3 ;
hence not 29 divides 5281 by NAT_4:9; :: thesis:
5281 = (31 * 170) + 11 ;
hence not 31 divides 5281 by NAT_4:9; :: thesis:
5281 = (37 * 142) + 27 ;
hence not 37 divides 5281 by NAT_4:9; :: thesis:
5281 = (41 * 128) + 33 ;
hence not 41 divides 5281 by NAT_4:9; :: thesis:
5281 = (43 * 122) + 35 ;
hence not 43 divides 5281 by NAT_4:9; :: thesis:
5281 = (47 * 112) + 17 ;
hence not 47 divides 5281 by NAT_4:9; :: thesis:
5281 = (53 * 99) + 34 ;
hence not 53 divides 5281 by NAT_4:9; :: thesis:
5281 = (59 * 89) + 30 ;
hence not 59 divides 5281 by NAT_4:9; :: thesis:
5281 = (61 * 86) + 35 ;
hence not 61 divides 5281 by NAT_4:9; :: thesis:
5281 = (67 * 78) + 55 ;
hence not 67 divides 5281 by NAT_4:9; :: thesis:
5281 = (71 * 74) + 27 ;
hence not 71 divides 5281 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5281 & n is prime holds
not n divides 5281 by XPRIMET1:40;
hence 5281 is prime by NAT_4:14; :: thesis: