
theorem
  5477 is prime
proof
  now
    5477 = 2*2738 + 1; hence not 2 divides 5477 by NAT_4:9;
    5477 = 3*1825 + 2; hence not 3 divides 5477 by NAT_4:9;
    5477 = 5*1095 + 2; hence not 5 divides 5477 by NAT_4:9;
    5477 = 7*782 + 3; hence not 7 divides 5477 by NAT_4:9;
    5477 = 11*497 + 10; hence not 11 divides 5477 by NAT_4:9;
    5477 = 13*421 + 4; hence not 13 divides 5477 by NAT_4:9;
    5477 = 17*322 + 3; hence not 17 divides 5477 by NAT_4:9;
    5477 = 19*288 + 5; hence not 19 divides 5477 by NAT_4:9;
    5477 = 23*238 + 3; hence not 23 divides 5477 by NAT_4:9;
    5477 = 29*188 + 25; hence not 29 divides 5477 by NAT_4:9;
    5477 = 31*176 + 21; hence not 31 divides 5477 by NAT_4:9;
    5477 = 37*148 + 1; hence not 37 divides 5477 by NAT_4:9;
    5477 = 41*133 + 24; hence not 41 divides 5477 by NAT_4:9;
    5477 = 43*127 + 16; hence not 43 divides 5477 by NAT_4:9;
    5477 = 47*116 + 25; hence not 47 divides 5477 by NAT_4:9;
    5477 = 53*103 + 18; hence not 53 divides 5477 by NAT_4:9;
    5477 = 59*92 + 49; hence not 59 divides 5477 by NAT_4:9;
    5477 = 61*89 + 48; hence not 61 divides 5477 by NAT_4:9;
    5477 = 67*81 + 50; hence not 67 divides 5477 by NAT_4:9;
    5477 = 71*77 + 10; hence not 71 divides 5477 by NAT_4:9;
    5477 = 73*75 + 2; hence not 73 divides 5477 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5477 & n is prime
  holds not n divides 5477 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
