
theorem
  1759 is prime
proof
  now
    1759 = 2*879 + 1; hence not 2 divides 1759 by NAT_4:9;
    1759 = 3*586 + 1; hence not 3 divides 1759 by NAT_4:9;
    1759 = 5*351 + 4; hence not 5 divides 1759 by NAT_4:9;
    1759 = 7*251 + 2; hence not 7 divides 1759 by NAT_4:9;
    1759 = 11*159 + 10; hence not 11 divides 1759 by NAT_4:9;
    1759 = 13*135 + 4; hence not 13 divides 1759 by NAT_4:9;
    1759 = 17*103 + 8; hence not 17 divides 1759 by NAT_4:9;
    1759 = 19*92 + 11; hence not 19 divides 1759 by NAT_4:9;
    1759 = 23*76 + 11; hence not 23 divides 1759 by NAT_4:9;
    1759 = 29*60 + 19; hence not 29 divides 1759 by NAT_4:9;
    1759 = 31*56 + 23; hence not 31 divides 1759 by NAT_4:9;
    1759 = 37*47 + 20; hence not 37 divides 1759 by NAT_4:9;
    1759 = 41*42 + 37; hence not 41 divides 1759 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1759 & n is prime
  holds not n divides 1759 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
