4241 = (2 * 2120) + 1 ;
hence not 2 divides 4241 by NAT_4:9; :: thesis:
4241 = (3 * 1413) + 2 ;
hence not 3 divides 4241 by NAT_4:9; :: thesis:
4241 = (5 * 848) + 1 ;
hence not 5 divides 4241 by NAT_4:9; :: thesis:
4241 = (7 * 605) + 6 ;
hence not 7 divides 4241 by NAT_4:9; :: thesis:
4241 = (11 * 385) + 6 ;
hence not 11 divides 4241 by NAT_4:9; :: thesis:
4241 = (13 * 326) + 3 ;
hence not 13 divides 4241 by NAT_4:9; :: thesis:
4241 = (17 * 249) + 8 ;
hence not 17 divides 4241 by NAT_4:9; :: thesis:
4241 = (19 * 223) + 4 ;
hence not 19 divides 4241 by NAT_4:9; :: thesis:
4241 = (23 * 184) + 9 ;
hence not 23 divides 4241 by NAT_4:9; :: thesis:
4241 = (29 * 146) + 7 ;
hence not 29 divides 4241 by NAT_4:9; :: thesis:
4241 = (31 * 136) + 25 ;
hence not 31 divides 4241 by NAT_4:9; :: thesis:
4241 = (37 * 114) + 23 ;
hence not 37 divides 4241 by NAT_4:9; :: thesis:
4241 = (41 * 103) + 18 ;
hence not 41 divides 4241 by NAT_4:9; :: thesis:
4241 = (43 * 98) + 27 ;
hence not 43 divides 4241 by NAT_4:9; :: thesis:
4241 = (47 * 90) + 11 ;
hence not 47 divides 4241 by NAT_4:9; :: thesis:
4241 = (53 * 80) + 1 ;
hence not 53 divides 4241 by NAT_4:9; :: thesis:
4241 = (59 * 71) + 52 ;
hence not 59 divides 4241 by NAT_4:9; :: thesis:
4241 = (61 * 69) + 32 ;
hence not 61 divides 4241 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 4241 & n is prime holds
not n divides 4241 by XPRIMET1:36;
hence 4241 is prime by NAT_4:14; :: thesis: