
theorem
  7517 is prime
proof
  now
    7517 = 2*3758 + 1; hence not 2 divides 7517 by NAT_4:9;
    7517 = 3*2505 + 2; hence not 3 divides 7517 by NAT_4:9;
    7517 = 5*1503 + 2; hence not 5 divides 7517 by NAT_4:9;
    7517 = 7*1073 + 6; hence not 7 divides 7517 by NAT_4:9;
    7517 = 11*683 + 4; hence not 11 divides 7517 by NAT_4:9;
    7517 = 13*578 + 3; hence not 13 divides 7517 by NAT_4:9;
    7517 = 17*442 + 3; hence not 17 divides 7517 by NAT_4:9;
    7517 = 19*395 + 12; hence not 19 divides 7517 by NAT_4:9;
    7517 = 23*326 + 19; hence not 23 divides 7517 by NAT_4:9;
    7517 = 29*259 + 6; hence not 29 divides 7517 by NAT_4:9;
    7517 = 31*242 + 15; hence not 31 divides 7517 by NAT_4:9;
    7517 = 37*203 + 6; hence not 37 divides 7517 by NAT_4:9;
    7517 = 41*183 + 14; hence not 41 divides 7517 by NAT_4:9;
    7517 = 43*174 + 35; hence not 43 divides 7517 by NAT_4:9;
    7517 = 47*159 + 44; hence not 47 divides 7517 by NAT_4:9;
    7517 = 53*141 + 44; hence not 53 divides 7517 by NAT_4:9;
    7517 = 59*127 + 24; hence not 59 divides 7517 by NAT_4:9;
    7517 = 61*123 + 14; hence not 61 divides 7517 by NAT_4:9;
    7517 = 67*112 + 13; hence not 67 divides 7517 by NAT_4:9;
    7517 = 71*105 + 62; hence not 71 divides 7517 by NAT_4:9;
    7517 = 73*102 + 71; hence not 73 divides 7517 by NAT_4:9;
    7517 = 79*95 + 12; hence not 79 divides 7517 by NAT_4:9;
    7517 = 83*90 + 47; hence not 83 divides 7517 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7517 & n is prime
  holds not n divides 7517 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
