
theorem
  8527 is prime
proof
  now
    8527 = 2*4263 + 1; hence not 2 divides 8527 by NAT_4:9;
    8527 = 3*2842 + 1; hence not 3 divides 8527 by NAT_4:9;
    8527 = 5*1705 + 2; hence not 5 divides 8527 by NAT_4:9;
    8527 = 7*1218 + 1; hence not 7 divides 8527 by NAT_4:9;
    8527 = 11*775 + 2; hence not 11 divides 8527 by NAT_4:9;
    8527 = 13*655 + 12; hence not 13 divides 8527 by NAT_4:9;
    8527 = 17*501 + 10; hence not 17 divides 8527 by NAT_4:9;
    8527 = 19*448 + 15; hence not 19 divides 8527 by NAT_4:9;
    8527 = 23*370 + 17; hence not 23 divides 8527 by NAT_4:9;
    8527 = 29*294 + 1; hence not 29 divides 8527 by NAT_4:9;
    8527 = 31*275 + 2; hence not 31 divides 8527 by NAT_4:9;
    8527 = 37*230 + 17; hence not 37 divides 8527 by NAT_4:9;
    8527 = 41*207 + 40; hence not 41 divides 8527 by NAT_4:9;
    8527 = 43*198 + 13; hence not 43 divides 8527 by NAT_4:9;
    8527 = 47*181 + 20; hence not 47 divides 8527 by NAT_4:9;
    8527 = 53*160 + 47; hence not 53 divides 8527 by NAT_4:9;
    8527 = 59*144 + 31; hence not 59 divides 8527 by NAT_4:9;
    8527 = 61*139 + 48; hence not 61 divides 8527 by NAT_4:9;
    8527 = 67*127 + 18; hence not 67 divides 8527 by NAT_4:9;
    8527 = 71*120 + 7; hence not 71 divides 8527 by NAT_4:9;
    8527 = 73*116 + 59; hence not 73 divides 8527 by NAT_4:9;
    8527 = 79*107 + 74; hence not 79 divides 8527 by NAT_4:9;
    8527 = 83*102 + 61; hence not 83 divides 8527 by NAT_4:9;
    8527 = 89*95 + 72; hence not 89 divides 8527 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8527 & n is prime
  holds not n divides 8527 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
