
theorem
  5233 is prime
proof
  now
    5233 = 2*2616 + 1; hence not 2 divides 5233 by NAT_4:9;
    5233 = 3*1744 + 1; hence not 3 divides 5233 by NAT_4:9;
    5233 = 5*1046 + 3; hence not 5 divides 5233 by NAT_4:9;
    5233 = 7*747 + 4; hence not 7 divides 5233 by NAT_4:9;
    5233 = 11*475 + 8; hence not 11 divides 5233 by NAT_4:9;
    5233 = 13*402 + 7; hence not 13 divides 5233 by NAT_4:9;
    5233 = 17*307 + 14; hence not 17 divides 5233 by NAT_4:9;
    5233 = 19*275 + 8; hence not 19 divides 5233 by NAT_4:9;
    5233 = 23*227 + 12; hence not 23 divides 5233 by NAT_4:9;
    5233 = 29*180 + 13; hence not 29 divides 5233 by NAT_4:9;
    5233 = 31*168 + 25; hence not 31 divides 5233 by NAT_4:9;
    5233 = 37*141 + 16; hence not 37 divides 5233 by NAT_4:9;
    5233 = 41*127 + 26; hence not 41 divides 5233 by NAT_4:9;
    5233 = 43*121 + 30; hence not 43 divides 5233 by NAT_4:9;
    5233 = 47*111 + 16; hence not 47 divides 5233 by NAT_4:9;
    5233 = 53*98 + 39; hence not 53 divides 5233 by NAT_4:9;
    5233 = 59*88 + 41; hence not 59 divides 5233 by NAT_4:9;
    5233 = 61*85 + 48; hence not 61 divides 5233 by NAT_4:9;
    5233 = 67*78 + 7; hence not 67 divides 5233 by NAT_4:9;
    5233 = 71*73 + 50; hence not 71 divides 5233 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5233 & n is prime
  holds not n divides 5233 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
