
theorem
  7229 is prime
proof
  now
    7229 = 2*3614 + 1; hence not 2 divides 7229 by NAT_4:9;
    7229 = 3*2409 + 2; hence not 3 divides 7229 by NAT_4:9;
    7229 = 5*1445 + 4; hence not 5 divides 7229 by NAT_4:9;
    7229 = 7*1032 + 5; hence not 7 divides 7229 by NAT_4:9;
    7229 = 11*657 + 2; hence not 11 divides 7229 by NAT_4:9;
    7229 = 13*556 + 1; hence not 13 divides 7229 by NAT_4:9;
    7229 = 17*425 + 4; hence not 17 divides 7229 by NAT_4:9;
    7229 = 19*380 + 9; hence not 19 divides 7229 by NAT_4:9;
    7229 = 23*314 + 7; hence not 23 divides 7229 by NAT_4:9;
    7229 = 29*249 + 8; hence not 29 divides 7229 by NAT_4:9;
    7229 = 31*233 + 6; hence not 31 divides 7229 by NAT_4:9;
    7229 = 37*195 + 14; hence not 37 divides 7229 by NAT_4:9;
    7229 = 41*176 + 13; hence not 41 divides 7229 by NAT_4:9;
    7229 = 43*168 + 5; hence not 43 divides 7229 by NAT_4:9;
    7229 = 47*153 + 38; hence not 47 divides 7229 by NAT_4:9;
    7229 = 53*136 + 21; hence not 53 divides 7229 by NAT_4:9;
    7229 = 59*122 + 31; hence not 59 divides 7229 by NAT_4:9;
    7229 = 61*118 + 31; hence not 61 divides 7229 by NAT_4:9;
    7229 = 67*107 + 60; hence not 67 divides 7229 by NAT_4:9;
    7229 = 71*101 + 58; hence not 71 divides 7229 by NAT_4:9;
    7229 = 73*99 + 2; hence not 73 divides 7229 by NAT_4:9;
    7229 = 79*91 + 40; hence not 79 divides 7229 by NAT_4:9;
    7229 = 83*87 + 8; hence not 83 divides 7229 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7229 & n is prime
  holds not n divides 7229 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
