
theorem
  7477 is prime
proof
  now
    7477 = 2*3738 + 1; hence not 2 divides 7477 by NAT_4:9;
    7477 = 3*2492 + 1; hence not 3 divides 7477 by NAT_4:9;
    7477 = 5*1495 + 2; hence not 5 divides 7477 by NAT_4:9;
    7477 = 7*1068 + 1; hence not 7 divides 7477 by NAT_4:9;
    7477 = 11*679 + 8; hence not 11 divides 7477 by NAT_4:9;
    7477 = 13*575 + 2; hence not 13 divides 7477 by NAT_4:9;
    7477 = 17*439 + 14; hence not 17 divides 7477 by NAT_4:9;
    7477 = 19*393 + 10; hence not 19 divides 7477 by NAT_4:9;
    7477 = 23*325 + 2; hence not 23 divides 7477 by NAT_4:9;
    7477 = 29*257 + 24; hence not 29 divides 7477 by NAT_4:9;
    7477 = 31*241 + 6; hence not 31 divides 7477 by NAT_4:9;
    7477 = 37*202 + 3; hence not 37 divides 7477 by NAT_4:9;
    7477 = 41*182 + 15; hence not 41 divides 7477 by NAT_4:9;
    7477 = 43*173 + 38; hence not 43 divides 7477 by NAT_4:9;
    7477 = 47*159 + 4; hence not 47 divides 7477 by NAT_4:9;
    7477 = 53*141 + 4; hence not 53 divides 7477 by NAT_4:9;
    7477 = 59*126 + 43; hence not 59 divides 7477 by NAT_4:9;
    7477 = 61*122 + 35; hence not 61 divides 7477 by NAT_4:9;
    7477 = 67*111 + 40; hence not 67 divides 7477 by NAT_4:9;
    7477 = 71*105 + 22; hence not 71 divides 7477 by NAT_4:9;
    7477 = 73*102 + 31; hence not 73 divides 7477 by NAT_4:9;
    7477 = 79*94 + 51; hence not 79 divides 7477 by NAT_4:9;
    7477 = 83*90 + 7; hence not 83 divides 7477 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7477 & n is prime
  holds not n divides 7477 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
