
theorem
  7499 is prime
proof
  now
    7499 = 2*3749 + 1; hence not 2 divides 7499 by NAT_4:9;
    7499 = 3*2499 + 2; hence not 3 divides 7499 by NAT_4:9;
    7499 = 5*1499 + 4; hence not 5 divides 7499 by NAT_4:9;
    7499 = 7*1071 + 2; hence not 7 divides 7499 by NAT_4:9;
    7499 = 11*681 + 8; hence not 11 divides 7499 by NAT_4:9;
    7499 = 13*576 + 11; hence not 13 divides 7499 by NAT_4:9;
    7499 = 17*441 + 2; hence not 17 divides 7499 by NAT_4:9;
    7499 = 19*394 + 13; hence not 19 divides 7499 by NAT_4:9;
    7499 = 23*326 + 1; hence not 23 divides 7499 by NAT_4:9;
    7499 = 29*258 + 17; hence not 29 divides 7499 by NAT_4:9;
    7499 = 31*241 + 28; hence not 31 divides 7499 by NAT_4:9;
    7499 = 37*202 + 25; hence not 37 divides 7499 by NAT_4:9;
    7499 = 41*182 + 37; hence not 41 divides 7499 by NAT_4:9;
    7499 = 43*174 + 17; hence not 43 divides 7499 by NAT_4:9;
    7499 = 47*159 + 26; hence not 47 divides 7499 by NAT_4:9;
    7499 = 53*141 + 26; hence not 53 divides 7499 by NAT_4:9;
    7499 = 59*127 + 6; hence not 59 divides 7499 by NAT_4:9;
    7499 = 61*122 + 57; hence not 61 divides 7499 by NAT_4:9;
    7499 = 67*111 + 62; hence not 67 divides 7499 by NAT_4:9;
    7499 = 71*105 + 44; hence not 71 divides 7499 by NAT_4:9;
    7499 = 73*102 + 53; hence not 73 divides 7499 by NAT_4:9;
    7499 = 79*94 + 73; hence not 79 divides 7499 by NAT_4:9;
    7499 = 83*90 + 29; hence not 83 divides 7499 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7499 & n is prime
  holds not n divides 7499 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
