
theorem
  7547 is prime
proof
  now
    7547 = 2*3773 + 1; hence not 2 divides 7547 by NAT_4:9;
    7547 = 3*2515 + 2; hence not 3 divides 7547 by NAT_4:9;
    7547 = 5*1509 + 2; hence not 5 divides 7547 by NAT_4:9;
    7547 = 7*1078 + 1; hence not 7 divides 7547 by NAT_4:9;
    7547 = 11*686 + 1; hence not 11 divides 7547 by NAT_4:9;
    7547 = 13*580 + 7; hence not 13 divides 7547 by NAT_4:9;
    7547 = 17*443 + 16; hence not 17 divides 7547 by NAT_4:9;
    7547 = 19*397 + 4; hence not 19 divides 7547 by NAT_4:9;
    7547 = 23*328 + 3; hence not 23 divides 7547 by NAT_4:9;
    7547 = 29*260 + 7; hence not 29 divides 7547 by NAT_4:9;
    7547 = 31*243 + 14; hence not 31 divides 7547 by NAT_4:9;
    7547 = 37*203 + 36; hence not 37 divides 7547 by NAT_4:9;
    7547 = 41*184 + 3; hence not 41 divides 7547 by NAT_4:9;
    7547 = 43*175 + 22; hence not 43 divides 7547 by NAT_4:9;
    7547 = 47*160 + 27; hence not 47 divides 7547 by NAT_4:9;
    7547 = 53*142 + 21; hence not 53 divides 7547 by NAT_4:9;
    7547 = 59*127 + 54; hence not 59 divides 7547 by NAT_4:9;
    7547 = 61*123 + 44; hence not 61 divides 7547 by NAT_4:9;
    7547 = 67*112 + 43; hence not 67 divides 7547 by NAT_4:9;
    7547 = 71*106 + 21; hence not 71 divides 7547 by NAT_4:9;
    7547 = 73*103 + 28; hence not 73 divides 7547 by NAT_4:9;
    7547 = 79*95 + 42; hence not 79 divides 7547 by NAT_4:9;
    7547 = 83*90 + 77; hence not 83 divides 7547 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7547 & n is prime
  holds not n divides 7547 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
