
theorem
  4231 is prime
proof
  now
    4231 = 2*2115 + 1; hence not 2 divides 4231 by NAT_4:9;
    4231 = 3*1410 + 1; hence not 3 divides 4231 by NAT_4:9;
    4231 = 5*846 + 1; hence not 5 divides 4231 by NAT_4:9;
    4231 = 7*604 + 3; hence not 7 divides 4231 by NAT_4:9;
    4231 = 11*384 + 7; hence not 11 divides 4231 by NAT_4:9;
    4231 = 13*325 + 6; hence not 13 divides 4231 by NAT_4:9;
    4231 = 17*248 + 15; hence not 17 divides 4231 by NAT_4:9;
    4231 = 19*222 + 13; hence not 19 divides 4231 by NAT_4:9;
    4231 = 23*183 + 22; hence not 23 divides 4231 by NAT_4:9;
    4231 = 29*145 + 26; hence not 29 divides 4231 by NAT_4:9;
    4231 = 31*136 + 15; hence not 31 divides 4231 by NAT_4:9;
    4231 = 37*114 + 13; hence not 37 divides 4231 by NAT_4:9;
    4231 = 41*103 + 8; hence not 41 divides 4231 by NAT_4:9;
    4231 = 43*98 + 17; hence not 43 divides 4231 by NAT_4:9;
    4231 = 47*90 + 1; hence not 47 divides 4231 by NAT_4:9;
    4231 = 53*79 + 44; hence not 53 divides 4231 by NAT_4:9;
    4231 = 59*71 + 42; hence not 59 divides 4231 by NAT_4:9;
    4231 = 61*69 + 22; hence not 61 divides 4231 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4231 & n is prime
  holds not n divides 4231 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
