
theorem
  4259 is prime
proof
  now
    4259 = 2*2129 + 1; hence not 2 divides 4259 by NAT_4:9;
    4259 = 3*1419 + 2; hence not 3 divides 4259 by NAT_4:9;
    4259 = 5*851 + 4; hence not 5 divides 4259 by NAT_4:9;
    4259 = 7*608 + 3; hence not 7 divides 4259 by NAT_4:9;
    4259 = 11*387 + 2; hence not 11 divides 4259 by NAT_4:9;
    4259 = 13*327 + 8; hence not 13 divides 4259 by NAT_4:9;
    4259 = 17*250 + 9; hence not 17 divides 4259 by NAT_4:9;
    4259 = 19*224 + 3; hence not 19 divides 4259 by NAT_4:9;
    4259 = 23*185 + 4; hence not 23 divides 4259 by NAT_4:9;
    4259 = 29*146 + 25; hence not 29 divides 4259 by NAT_4:9;
    4259 = 31*137 + 12; hence not 31 divides 4259 by NAT_4:9;
    4259 = 37*115 + 4; hence not 37 divides 4259 by NAT_4:9;
    4259 = 41*103 + 36; hence not 41 divides 4259 by NAT_4:9;
    4259 = 43*99 + 2; hence not 43 divides 4259 by NAT_4:9;
    4259 = 47*90 + 29; hence not 47 divides 4259 by NAT_4:9;
    4259 = 53*80 + 19; hence not 53 divides 4259 by NAT_4:9;
    4259 = 59*72 + 11; hence not 59 divides 4259 by NAT_4:9;
    4259 = 61*69 + 50; hence not 61 divides 4259 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4259 & n is prime
  holds not n divides 4259 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
