
theorem
  4253 is prime
proof
  now
    4253 = 2*2126 + 1; hence not 2 divides 4253 by NAT_4:9;
    4253 = 3*1417 + 2; hence not 3 divides 4253 by NAT_4:9;
    4253 = 5*850 + 3; hence not 5 divides 4253 by NAT_4:9;
    4253 = 7*607 + 4; hence not 7 divides 4253 by NAT_4:9;
    4253 = 11*386 + 7; hence not 11 divides 4253 by NAT_4:9;
    4253 = 13*327 + 2; hence not 13 divides 4253 by NAT_4:9;
    4253 = 17*250 + 3; hence not 17 divides 4253 by NAT_4:9;
    4253 = 19*223 + 16; hence not 19 divides 4253 by NAT_4:9;
    4253 = 23*184 + 21; hence not 23 divides 4253 by NAT_4:9;
    4253 = 29*146 + 19; hence not 29 divides 4253 by NAT_4:9;
    4253 = 31*137 + 6; hence not 31 divides 4253 by NAT_4:9;
    4253 = 37*114 + 35; hence not 37 divides 4253 by NAT_4:9;
    4253 = 41*103 + 30; hence not 41 divides 4253 by NAT_4:9;
    4253 = 43*98 + 39; hence not 43 divides 4253 by NAT_4:9;
    4253 = 47*90 + 23; hence not 47 divides 4253 by NAT_4:9;
    4253 = 53*80 + 13; hence not 53 divides 4253 by NAT_4:9;
    4253 = 59*72 + 5; hence not 59 divides 4253 by NAT_4:9;
    4253 = 61*69 + 44; hence not 61 divides 4253 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4253 & n is prime
  holds not n divides 4253 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
