5879 = (2 * 2939) + 1 ;
hence not 2 divides 5879 by NAT_4:9; :: thesis:
5879 = (3 * 1959) + 2 ;
hence not 3 divides 5879 by NAT_4:9; :: thesis:
5879 = (5 * 1175) + 4 ;
hence not 5 divides 5879 by NAT_4:9; :: thesis:
5879 = (7 * 839) + 6 ;
hence not 7 divides 5879 by NAT_4:9; :: thesis:
5879 = (11 * 534) + 5 ;
hence not 11 divides 5879 by NAT_4:9; :: thesis:
5879 = (13 * 452) + 3 ;
hence not 13 divides 5879 by NAT_4:9; :: thesis:
5879 = (17 * 345) + 14 ;
hence not 17 divides 5879 by NAT_4:9; :: thesis:
5879 = (19 * 309) + 8 ;
hence not 19 divides 5879 by NAT_4:9; :: thesis:
5879 = (23 * 255) + 14 ;
hence not 23 divides 5879 by NAT_4:9; :: thesis:
5879 = (29 * 202) + 21 ;
hence not 29 divides 5879 by NAT_4:9; :: thesis:
5879 = (31 * 189) + 20 ;
hence not 31 divides 5879 by NAT_4:9; :: thesis:
5879 = (37 * 158) + 33 ;
hence not 37 divides 5879 by NAT_4:9; :: thesis:
5879 = (41 * 143) + 16 ;
hence not 41 divides 5879 by NAT_4:9; :: thesis:
5879 = (43 * 136) + 31 ;
hence not 43 divides 5879 by NAT_4:9; :: thesis:
5879 = (47 * 125) + 4 ;
hence not 47 divides 5879 by NAT_4:9; :: thesis:
5879 = (53 * 110) + 49 ;
hence not 53 divides 5879 by NAT_4:9; :: thesis:
5879 = (59 * 99) + 38 ;
hence not 59 divides 5879 by NAT_4:9; :: thesis:
5879 = (61 * 96) + 23 ;
hence not 61 divides 5879 by NAT_4:9; :: thesis:
5879 = (67 * 87) + 50 ;
hence not 67 divides 5879 by NAT_4:9; :: thesis:
5879 = (71 * 82) + 57 ;
hence not 71 divides 5879 by NAT_4:9; :: thesis:
5879 = (73 * 80) + 39 ;
hence not 73 divides 5879 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5879 & n is prime holds
not n divides 5879 by XPRIMET1:42;
hence 5879 is prime by NAT_4:14; :: thesis: