
theorem
  3529 is prime
proof
  now
    3529 = 2*1764 + 1; hence not 2 divides 3529 by NAT_4:9;
    3529 = 3*1176 + 1; hence not 3 divides 3529 by NAT_4:9;
    3529 = 5*705 + 4; hence not 5 divides 3529 by NAT_4:9;
    3529 = 7*504 + 1; hence not 7 divides 3529 by NAT_4:9;
    3529 = 11*320 + 9; hence not 11 divides 3529 by NAT_4:9;
    3529 = 13*271 + 6; hence not 13 divides 3529 by NAT_4:9;
    3529 = 17*207 + 10; hence not 17 divides 3529 by NAT_4:9;
    3529 = 19*185 + 14; hence not 19 divides 3529 by NAT_4:9;
    3529 = 23*153 + 10; hence not 23 divides 3529 by NAT_4:9;
    3529 = 29*121 + 20; hence not 29 divides 3529 by NAT_4:9;
    3529 = 31*113 + 26; hence not 31 divides 3529 by NAT_4:9;
    3529 = 37*95 + 14; hence not 37 divides 3529 by NAT_4:9;
    3529 = 41*86 + 3; hence not 41 divides 3529 by NAT_4:9;
    3529 = 43*82 + 3; hence not 43 divides 3529 by NAT_4:9;
    3529 = 47*75 + 4; hence not 47 divides 3529 by NAT_4:9;
    3529 = 53*66 + 31; hence not 53 divides 3529 by NAT_4:9;
    3529 = 59*59 + 48; hence not 59 divides 3529 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3529 & n is prime
  holds not n divides 3529 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
