
theorem
  9277 is prime
proof
  now
    9277 = 2*4638 + 1; hence not 2 divides 9277 by NAT_4:9;
    9277 = 3*3092 + 1; hence not 3 divides 9277 by NAT_4:9;
    9277 = 5*1855 + 2; hence not 5 divides 9277 by NAT_4:9;
    9277 = 7*1325 + 2; hence not 7 divides 9277 by NAT_4:9;
    9277 = 11*843 + 4; hence not 11 divides 9277 by NAT_4:9;
    9277 = 13*713 + 8; hence not 13 divides 9277 by NAT_4:9;
    9277 = 17*545 + 12; hence not 17 divides 9277 by NAT_4:9;
    9277 = 19*488 + 5; hence not 19 divides 9277 by NAT_4:9;
    9277 = 23*403 + 8; hence not 23 divides 9277 by NAT_4:9;
    9277 = 29*319 + 26; hence not 29 divides 9277 by NAT_4:9;
    9277 = 31*299 + 8; hence not 31 divides 9277 by NAT_4:9;
    9277 = 37*250 + 27; hence not 37 divides 9277 by NAT_4:9;
    9277 = 41*226 + 11; hence not 41 divides 9277 by NAT_4:9;
    9277 = 43*215 + 32; hence not 43 divides 9277 by NAT_4:9;
    9277 = 47*197 + 18; hence not 47 divides 9277 by NAT_4:9;
    9277 = 53*175 + 2; hence not 53 divides 9277 by NAT_4:9;
    9277 = 59*157 + 14; hence not 59 divides 9277 by NAT_4:9;
    9277 = 61*152 + 5; hence not 61 divides 9277 by NAT_4:9;
    9277 = 67*138 + 31; hence not 67 divides 9277 by NAT_4:9;
    9277 = 71*130 + 47; hence not 71 divides 9277 by NAT_4:9;
    9277 = 73*127 + 6; hence not 73 divides 9277 by NAT_4:9;
    9277 = 79*117 + 34; hence not 79 divides 9277 by NAT_4:9;
    9277 = 83*111 + 64; hence not 83 divides 9277 by NAT_4:9;
    9277 = 89*104 + 21; hence not 89 divides 9277 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9277 & n is prime
  holds not n divides 9277 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
