
theorem
  5227 is prime
proof
  now
    5227 = 2*2613 + 1; hence not 2 divides 5227 by NAT_4:9;
    5227 = 3*1742 + 1; hence not 3 divides 5227 by NAT_4:9;
    5227 = 5*1045 + 2; hence not 5 divides 5227 by NAT_4:9;
    5227 = 7*746 + 5; hence not 7 divides 5227 by NAT_4:9;
    5227 = 11*475 + 2; hence not 11 divides 5227 by NAT_4:9;
    5227 = 13*402 + 1; hence not 13 divides 5227 by NAT_4:9;
    5227 = 17*307 + 8; hence not 17 divides 5227 by NAT_4:9;
    5227 = 19*275 + 2; hence not 19 divides 5227 by NAT_4:9;
    5227 = 23*227 + 6; hence not 23 divides 5227 by NAT_4:9;
    5227 = 29*180 + 7; hence not 29 divides 5227 by NAT_4:9;
    5227 = 31*168 + 19; hence not 31 divides 5227 by NAT_4:9;
    5227 = 37*141 + 10; hence not 37 divides 5227 by NAT_4:9;
    5227 = 41*127 + 20; hence not 41 divides 5227 by NAT_4:9;
    5227 = 43*121 + 24; hence not 43 divides 5227 by NAT_4:9;
    5227 = 47*111 + 10; hence not 47 divides 5227 by NAT_4:9;
    5227 = 53*98 + 33; hence not 53 divides 5227 by NAT_4:9;
    5227 = 59*88 + 35; hence not 59 divides 5227 by NAT_4:9;
    5227 = 61*85 + 42; hence not 61 divides 5227 by NAT_4:9;
    5227 = 67*78 + 1; hence not 67 divides 5227 by NAT_4:9;
    5227 = 71*73 + 44; hence not 71 divides 5227 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5227 & n is prime
  holds not n divides 5227 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
