5477 = (2 * 2738) + 1 ;
hence not 2 divides 5477 by NAT_4:9; :: thesis:
5477 = (3 * 1825) + 2 ;
hence not 3 divides 5477 by NAT_4:9; :: thesis:
5477 = (5 * 1095) + 2 ;
hence not 5 divides 5477 by NAT_4:9; :: thesis:
5477 = (7 * 782) + 3 ;
hence not 7 divides 5477 by NAT_4:9; :: thesis:
5477 = (11 * 497) + 10 ;
hence not 11 divides 5477 by NAT_4:9; :: thesis:
5477 = (13 * 421) + 4 ;
hence not 13 divides 5477 by NAT_4:9; :: thesis:
5477 = (17 * 322) + 3 ;
hence not 17 divides 5477 by NAT_4:9; :: thesis:
5477 = (19 * 288) + 5 ;
hence not 19 divides 5477 by NAT_4:9; :: thesis:
5477 = (23 * 238) + 3 ;
hence not 23 divides 5477 by NAT_4:9; :: thesis:
5477 = (29 * 188) + 25 ;
hence not 29 divides 5477 by NAT_4:9; :: thesis:
5477 = (31 * 176) + 21 ;
hence not 31 divides 5477 by NAT_4:9; :: thesis:
5477 = (37 * 148) + 1 ;
hence not 37 divides 5477 by NAT_4:9; :: thesis:
5477 = (41 * 133) + 24 ;
hence not 41 divides 5477 by NAT_4:9; :: thesis:
5477 = (43 * 127) + 16 ;
hence not 43 divides 5477 by NAT_4:9; :: thesis:
5477 = (47 * 116) + 25 ;
hence not 47 divides 5477 by NAT_4:9; :: thesis:
5477 = (53 * 103) + 18 ;
hence not 53 divides 5477 by NAT_4:9; :: thesis:
5477 = (59 * 92) + 49 ;
hence not 59 divides 5477 by NAT_4:9; :: thesis:
5477 = (61 * 89) + 48 ;
hence not 61 divides 5477 by NAT_4:9; :: thesis:
5477 = (67 * 81) + 50 ;
hence not 67 divides 5477 by NAT_4:9; :: thesis:
5477 = (71 * 77) + 10 ;
hence not 71 divides 5477 by NAT_4:9; :: thesis:
5477 = (73 * 75) + 2 ;
hence not 73 divides 5477 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5477 & n is prime holds
not n divides 5477 by XPRIMET1:42;
hence 5477 is prime by NAT_4:14; :: thesis: