4231 = (2 * 2115) + 1 ;
hence not 2 divides 4231 by NAT_4:9; :: thesis:
4231 = (3 * 1410) + 1 ;
hence not 3 divides 4231 by NAT_4:9; :: thesis:
4231 = (5 * 846) + 1 ;
hence not 5 divides 4231 by NAT_4:9; :: thesis:
4231 = (7 * 604) + 3 ;
hence not 7 divides 4231 by NAT_4:9; :: thesis:
4231 = (11 * 384) + 7 ;
hence not 11 divides 4231 by NAT_4:9; :: thesis:
4231 = (13 * 325) + 6 ;
hence not 13 divides 4231 by NAT_4:9; :: thesis:
4231 = (17 * 248) + 15 ;
hence not 17 divides 4231 by NAT_4:9; :: thesis:
4231 = (19 * 222) + 13 ;
hence not 19 divides 4231 by NAT_4:9; :: thesis:
4231 = (23 * 183) + 22 ;
hence not 23 divides 4231 by NAT_4:9; :: thesis:
4231 = (29 * 145) + 26 ;
hence not 29 divides 4231 by NAT_4:9; :: thesis:
4231 = (31 * 136) + 15 ;
hence not 31 divides 4231 by NAT_4:9; :: thesis:
4231 = (37 * 114) + 13 ;
hence not 37 divides 4231 by NAT_4:9; :: thesis:
4231 = (41 * 103) + 8 ;
hence not 41 divides 4231 by NAT_4:9; :: thesis:
4231 = (43 * 98) + 17 ;
hence not 43 divides 4231 by NAT_4:9; :: thesis:
4231 = (47 * 90) + 1 ;
hence not 47 divides 4231 by NAT_4:9; :: thesis:
4231 = (53 * 79) + 44 ;
hence not 53 divides 4231 by NAT_4:9; :: thesis:
4231 = (59 * 71) + 42 ;
hence not 59 divides 4231 by NAT_4:9; :: thesis:
4231 = (61 * 69) + 22 ;
hence not 61 divides 4231 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 4231 & n is prime holds
not n divides 4231 by XPRIMET1:36;
hence 4231 is prime by NAT_4:14; :: thesis: