
theorem
  7523 is prime
proof
  now
    7523 = 2*3761 + 1; hence not 2 divides 7523 by NAT_4:9;
    7523 = 3*2507 + 2; hence not 3 divides 7523 by NAT_4:9;
    7523 = 5*1504 + 3; hence not 5 divides 7523 by NAT_4:9;
    7523 = 7*1074 + 5; hence not 7 divides 7523 by NAT_4:9;
    7523 = 11*683 + 10; hence not 11 divides 7523 by NAT_4:9;
    7523 = 13*578 + 9; hence not 13 divides 7523 by NAT_4:9;
    7523 = 17*442 + 9; hence not 17 divides 7523 by NAT_4:9;
    7523 = 19*395 + 18; hence not 19 divides 7523 by NAT_4:9;
    7523 = 23*327 + 2; hence not 23 divides 7523 by NAT_4:9;
    7523 = 29*259 + 12; hence not 29 divides 7523 by NAT_4:9;
    7523 = 31*242 + 21; hence not 31 divides 7523 by NAT_4:9;
    7523 = 37*203 + 12; hence not 37 divides 7523 by NAT_4:9;
    7523 = 41*183 + 20; hence not 41 divides 7523 by NAT_4:9;
    7523 = 43*174 + 41; hence not 43 divides 7523 by NAT_4:9;
    7523 = 47*160 + 3; hence not 47 divides 7523 by NAT_4:9;
    7523 = 53*141 + 50; hence not 53 divides 7523 by NAT_4:9;
    7523 = 59*127 + 30; hence not 59 divides 7523 by NAT_4:9;
    7523 = 61*123 + 20; hence not 61 divides 7523 by NAT_4:9;
    7523 = 67*112 + 19; hence not 67 divides 7523 by NAT_4:9;
    7523 = 71*105 + 68; hence not 71 divides 7523 by NAT_4:9;
    7523 = 73*103 + 4; hence not 73 divides 7523 by NAT_4:9;
    7523 = 79*95 + 18; hence not 79 divides 7523 by NAT_4:9;
    7523 = 83*90 + 53; hence not 83 divides 7523 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7523 & n is prime
  holds not n divides 7523 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
