
theorem
  8521 is prime
proof
  now
    8521 = 2*4260 + 1; hence not 2 divides 8521 by NAT_4:9;
    8521 = 3*2840 + 1; hence not 3 divides 8521 by NAT_4:9;
    8521 = 5*1704 + 1; hence not 5 divides 8521 by NAT_4:9;
    8521 = 7*1217 + 2; hence not 7 divides 8521 by NAT_4:9;
    8521 = 11*774 + 7; hence not 11 divides 8521 by NAT_4:9;
    8521 = 13*655 + 6; hence not 13 divides 8521 by NAT_4:9;
    8521 = 17*501 + 4; hence not 17 divides 8521 by NAT_4:9;
    8521 = 19*448 + 9; hence not 19 divides 8521 by NAT_4:9;
    8521 = 23*370 + 11; hence not 23 divides 8521 by NAT_4:9;
    8521 = 29*293 + 24; hence not 29 divides 8521 by NAT_4:9;
    8521 = 31*274 + 27; hence not 31 divides 8521 by NAT_4:9;
    8521 = 37*230 + 11; hence not 37 divides 8521 by NAT_4:9;
    8521 = 41*207 + 34; hence not 41 divides 8521 by NAT_4:9;
    8521 = 43*198 + 7; hence not 43 divides 8521 by NAT_4:9;
    8521 = 47*181 + 14; hence not 47 divides 8521 by NAT_4:9;
    8521 = 53*160 + 41; hence not 53 divides 8521 by NAT_4:9;
    8521 = 59*144 + 25; hence not 59 divides 8521 by NAT_4:9;
    8521 = 61*139 + 42; hence not 61 divides 8521 by NAT_4:9;
    8521 = 67*127 + 12; hence not 67 divides 8521 by NAT_4:9;
    8521 = 71*120 + 1; hence not 71 divides 8521 by NAT_4:9;
    8521 = 73*116 + 53; hence not 73 divides 8521 by NAT_4:9;
    8521 = 79*107 + 68; hence not 79 divides 8521 by NAT_4:9;
    8521 = 83*102 + 55; hence not 83 divides 8521 by NAT_4:9;
    8521 = 89*95 + 66; hence not 89 divides 8521 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8521 & n is prime
  holds not n divides 8521 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
