
theorem
  5437 is prime
proof
  now
    5437 = 2*2718 + 1; hence not 2 divides 5437 by NAT_4:9;
    5437 = 3*1812 + 1; hence not 3 divides 5437 by NAT_4:9;
    5437 = 5*1087 + 2; hence not 5 divides 5437 by NAT_4:9;
    5437 = 7*776 + 5; hence not 7 divides 5437 by NAT_4:9;
    5437 = 11*494 + 3; hence not 11 divides 5437 by NAT_4:9;
    5437 = 13*418 + 3; hence not 13 divides 5437 by NAT_4:9;
    5437 = 17*319 + 14; hence not 17 divides 5437 by NAT_4:9;
    5437 = 19*286 + 3; hence not 19 divides 5437 by NAT_4:9;
    5437 = 23*236 + 9; hence not 23 divides 5437 by NAT_4:9;
    5437 = 29*187 + 14; hence not 29 divides 5437 by NAT_4:9;
    5437 = 31*175 + 12; hence not 31 divides 5437 by NAT_4:9;
    5437 = 37*146 + 35; hence not 37 divides 5437 by NAT_4:9;
    5437 = 41*132 + 25; hence not 41 divides 5437 by NAT_4:9;
    5437 = 43*126 + 19; hence not 43 divides 5437 by NAT_4:9;
    5437 = 47*115 + 32; hence not 47 divides 5437 by NAT_4:9;
    5437 = 53*102 + 31; hence not 53 divides 5437 by NAT_4:9;
    5437 = 59*92 + 9; hence not 59 divides 5437 by NAT_4:9;
    5437 = 61*89 + 8; hence not 61 divides 5437 by NAT_4:9;
    5437 = 67*81 + 10; hence not 67 divides 5437 by NAT_4:9;
    5437 = 71*76 + 41; hence not 71 divides 5437 by NAT_4:9;
    5437 = 73*74 + 35; hence not 73 divides 5437 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5437 & n is prime
  holds not n divides 5437 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
