1481 = (2 * 740) + 1 ;
hence not 2 divides 1481 by NAT_4:9; :: thesis:
1481 = (3 * 493) + 2 ;
hence not 3 divides 1481 by NAT_4:9; :: thesis:
1481 = (5 * 296) + 1 ;
hence not 5 divides 1481 by NAT_4:9; :: thesis:
1481 = (7 * 211) + 4 ;
hence not 7 divides 1481 by NAT_4:9; :: thesis:
1481 = (11 * 134) + 7 ;
hence not 11 divides 1481 by NAT_4:9; :: thesis:
1481 = (13 * 113) + 12 ;
hence not 13 divides 1481 by NAT_4:9; :: thesis:
1481 = (17 * 87) + 2 ;
hence not 17 divides 1481 by NAT_4:9; :: thesis:
1481 = (19 * 77) + 18 ;
hence not 19 divides 1481 by NAT_4:9; :: thesis:
1481 = (23 * 64) + 9 ;
hence not 23 divides 1481 by NAT_4:9; :: thesis:
1481 = (29 * 51) + 2 ;
hence not 29 divides 1481 by NAT_4:9; :: thesis:
1481 = (31 * 47) + 24 ;
hence not 31 divides 1481 by NAT_4:9; :: thesis:
1481 = (37 * 40) + 1 ;
hence not 37 divides 1481 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1481 & n is prime holds
not n divides 1481 by XPRIMET1:24;
hence 1481 is prime by NAT_4:14; :: thesis: