5479 = (2 * 2739) + 1 ;
hence not 2 divides 5479 by NAT_4:9; :: thesis:
5479 = (3 * 1826) + 1 ;
hence not 3 divides 5479 by NAT_4:9; :: thesis:
5479 = (5 * 1095) + 4 ;
hence not 5 divides 5479 by NAT_4:9; :: thesis:
5479 = (7 * 782) + 5 ;
hence not 7 divides 5479 by NAT_4:9; :: thesis:
5479 = (11 * 498) + 1 ;
hence not 11 divides 5479 by NAT_4:9; :: thesis:
5479 = (13 * 421) + 6 ;
hence not 13 divides 5479 by NAT_4:9; :: thesis:
5479 = (17 * 322) + 5 ;
hence not 17 divides 5479 by NAT_4:9; :: thesis:
5479 = (19 * 288) + 7 ;
hence not 19 divides 5479 by NAT_4:9; :: thesis:
5479 = (23 * 238) + 5 ;
hence not 23 divides 5479 by NAT_4:9; :: thesis:
5479 = (29 * 188) + 27 ;
hence not 29 divides 5479 by NAT_4:9; :: thesis:
5479 = (31 * 176) + 23 ;
hence not 31 divides 5479 by NAT_4:9; :: thesis:
5479 = (37 * 148) + 3 ;
hence not 37 divides 5479 by NAT_4:9; :: thesis:
5479 = (41 * 133) + 26 ;
hence not 41 divides 5479 by NAT_4:9; :: thesis:
5479 = (43 * 127) + 18 ;
hence not 43 divides 5479 by NAT_4:9; :: thesis:
5479 = (47 * 116) + 27 ;
hence not 47 divides 5479 by NAT_4:9; :: thesis:
5479 = (53 * 103) + 20 ;
hence not 53 divides 5479 by NAT_4:9; :: thesis:
5479 = (59 * 92) + 51 ;
hence not 59 divides 5479 by NAT_4:9; :: thesis:
5479 = (61 * 89) + 50 ;
hence not 61 divides 5479 by NAT_4:9; :: thesis:
5479 = (67 * 81) + 52 ;
hence not 67 divides 5479 by NAT_4:9; :: thesis:
5479 = (71 * 77) + 12 ;
hence not 71 divides 5479 by NAT_4:9; :: thesis:
5479 = (73 * 75) + 4 ;
hence not 73 divides 5479 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5479 & n is prime holds
not n divides 5479 by XPRIMET1:42;
hence 5479 is prime by NAT_4:14; :: thesis: