
theorem
  3533 is prime
proof
  now
    3533 = 2*1766 + 1; hence not 2 divides 3533 by NAT_4:9;
    3533 = 3*1177 + 2; hence not 3 divides 3533 by NAT_4:9;
    3533 = 5*706 + 3; hence not 5 divides 3533 by NAT_4:9;
    3533 = 7*504 + 5; hence not 7 divides 3533 by NAT_4:9;
    3533 = 11*321 + 2; hence not 11 divides 3533 by NAT_4:9;
    3533 = 13*271 + 10; hence not 13 divides 3533 by NAT_4:9;
    3533 = 17*207 + 14; hence not 17 divides 3533 by NAT_4:9;
    3533 = 19*185 + 18; hence not 19 divides 3533 by NAT_4:9;
    3533 = 23*153 + 14; hence not 23 divides 3533 by NAT_4:9;
    3533 = 29*121 + 24; hence not 29 divides 3533 by NAT_4:9;
    3533 = 31*113 + 30; hence not 31 divides 3533 by NAT_4:9;
    3533 = 37*95 + 18; hence not 37 divides 3533 by NAT_4:9;
    3533 = 41*86 + 7; hence not 41 divides 3533 by NAT_4:9;
    3533 = 43*82 + 7; hence not 43 divides 3533 by NAT_4:9;
    3533 = 47*75 + 8; hence not 47 divides 3533 by NAT_4:9;
    3533 = 53*66 + 35; hence not 53 divides 3533 by NAT_4:9;
    3533 = 59*59 + 52; hence not 59 divides 3533 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3533 & n is prime
  holds not n divides 3533 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
