3593 = (2 * 1796) + 1 ;
hence not 2 divides 3593 by NAT_4:9; :: thesis:
3593 = (3 * 1197) + 2 ;
hence not 3 divides 3593 by NAT_4:9; :: thesis:
3593 = (5 * 718) + 3 ;
hence not 5 divides 3593 by NAT_4:9; :: thesis:
3593 = (7 * 513) + 2 ;
hence not 7 divides 3593 by NAT_4:9; :: thesis:
3593 = (11 * 326) + 7 ;
hence not 11 divides 3593 by NAT_4:9; :: thesis:
3593 = (13 * 276) + 5 ;
hence not 13 divides 3593 by NAT_4:9; :: thesis:
3593 = (17 * 211) + 6 ;
hence not 17 divides 3593 by NAT_4:9; :: thesis:
3593 = (19 * 189) + 2 ;
hence not 19 divides 3593 by NAT_4:9; :: thesis:
3593 = (23 * 156) + 5 ;
hence not 23 divides 3593 by NAT_4:9; :: thesis:
3593 = (29 * 123) + 26 ;
hence not 29 divides 3593 by NAT_4:9; :: thesis:
3593 = (31 * 115) + 28 ;
hence not 31 divides 3593 by NAT_4:9; :: thesis:
3593 = (37 * 97) + 4 ;
hence not 37 divides 3593 by NAT_4:9; :: thesis:
3593 = (41 * 87) + 26 ;
hence not 41 divides 3593 by NAT_4:9; :: thesis:
3593 = (43 * 83) + 24 ;
hence not 43 divides 3593 by NAT_4:9; :: thesis:
3593 = (47 * 76) + 21 ;
hence not 47 divides 3593 by NAT_4:9; :: thesis:
3593 = (53 * 67) + 42 ;
hence not 53 divides 3593 by NAT_4:9; :: thesis:
3593 = (59 * 60) + 53 ;
hence not 59 divides 3593 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3593 & n is prime holds
not n divides 3593 by XPRIMET1:34;
hence 3593 is prime by NAT_4:14; :: thesis: