
theorem
  8513 is prime
proof
  now
    8513 = 2*4256 + 1; hence not 2 divides 8513 by NAT_4:9;
    8513 = 3*2837 + 2; hence not 3 divides 8513 by NAT_4:9;
    8513 = 5*1702 + 3; hence not 5 divides 8513 by NAT_4:9;
    8513 = 7*1216 + 1; hence not 7 divides 8513 by NAT_4:9;
    8513 = 11*773 + 10; hence not 11 divides 8513 by NAT_4:9;
    8513 = 13*654 + 11; hence not 13 divides 8513 by NAT_4:9;
    8513 = 17*500 + 13; hence not 17 divides 8513 by NAT_4:9;
    8513 = 19*448 + 1; hence not 19 divides 8513 by NAT_4:9;
    8513 = 23*370 + 3; hence not 23 divides 8513 by NAT_4:9;
    8513 = 29*293 + 16; hence not 29 divides 8513 by NAT_4:9;
    8513 = 31*274 + 19; hence not 31 divides 8513 by NAT_4:9;
    8513 = 37*230 + 3; hence not 37 divides 8513 by NAT_4:9;
    8513 = 41*207 + 26; hence not 41 divides 8513 by NAT_4:9;
    8513 = 43*197 + 42; hence not 43 divides 8513 by NAT_4:9;
    8513 = 47*181 + 6; hence not 47 divides 8513 by NAT_4:9;
    8513 = 53*160 + 33; hence not 53 divides 8513 by NAT_4:9;
    8513 = 59*144 + 17; hence not 59 divides 8513 by NAT_4:9;
    8513 = 61*139 + 34; hence not 61 divides 8513 by NAT_4:9;
    8513 = 67*127 + 4; hence not 67 divides 8513 by NAT_4:9;
    8513 = 71*119 + 64; hence not 71 divides 8513 by NAT_4:9;
    8513 = 73*116 + 45; hence not 73 divides 8513 by NAT_4:9;
    8513 = 79*107 + 60; hence not 79 divides 8513 by NAT_4:9;
    8513 = 83*102 + 47; hence not 83 divides 8513 by NAT_4:9;
    8513 = 89*95 + 58; hence not 89 divides 8513 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8513 & n is prime
  holds not n divides 8513 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
