
theorem
  7541 is prime
proof
  now
    7541 = 2*3770 + 1; hence not 2 divides 7541 by NAT_4:9;
    7541 = 3*2513 + 2; hence not 3 divides 7541 by NAT_4:9;
    7541 = 5*1508 + 1; hence not 5 divides 7541 by NAT_4:9;
    7541 = 7*1077 + 2; hence not 7 divides 7541 by NAT_4:9;
    7541 = 11*685 + 6; hence not 11 divides 7541 by NAT_4:9;
    7541 = 13*580 + 1; hence not 13 divides 7541 by NAT_4:9;
    7541 = 17*443 + 10; hence not 17 divides 7541 by NAT_4:9;
    7541 = 19*396 + 17; hence not 19 divides 7541 by NAT_4:9;
    7541 = 23*327 + 20; hence not 23 divides 7541 by NAT_4:9;
    7541 = 29*260 + 1; hence not 29 divides 7541 by NAT_4:9;
    7541 = 31*243 + 8; hence not 31 divides 7541 by NAT_4:9;
    7541 = 37*203 + 30; hence not 37 divides 7541 by NAT_4:9;
    7541 = 41*183 + 38; hence not 41 divides 7541 by NAT_4:9;
    7541 = 43*175 + 16; hence not 43 divides 7541 by NAT_4:9;
    7541 = 47*160 + 21; hence not 47 divides 7541 by NAT_4:9;
    7541 = 53*142 + 15; hence not 53 divides 7541 by NAT_4:9;
    7541 = 59*127 + 48; hence not 59 divides 7541 by NAT_4:9;
    7541 = 61*123 + 38; hence not 61 divides 7541 by NAT_4:9;
    7541 = 67*112 + 37; hence not 67 divides 7541 by NAT_4:9;
    7541 = 71*106 + 15; hence not 71 divides 7541 by NAT_4:9;
    7541 = 73*103 + 22; hence not 73 divides 7541 by NAT_4:9;
    7541 = 79*95 + 36; hence not 79 divides 7541 by NAT_4:9;
    7541 = 83*90 + 71; hence not 83 divides 7541 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7541 & n is prime
  holds not n divides 7541 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
