
theorem
  1783 is prime
proof
  now
    1783 = 2*891 + 1; hence not 2 divides 1783 by NAT_4:9;
    1783 = 3*594 + 1; hence not 3 divides 1783 by NAT_4:9;
    1783 = 5*356 + 3; hence not 5 divides 1783 by NAT_4:9;
    1783 = 7*254 + 5; hence not 7 divides 1783 by NAT_4:9;
    1783 = 11*162 + 1; hence not 11 divides 1783 by NAT_4:9;
    1783 = 13*137 + 2; hence not 13 divides 1783 by NAT_4:9;
    1783 = 17*104 + 15; hence not 17 divides 1783 by NAT_4:9;
    1783 = 19*93 + 16; hence not 19 divides 1783 by NAT_4:9;
    1783 = 23*77 + 12; hence not 23 divides 1783 by NAT_4:9;
    1783 = 29*61 + 14; hence not 29 divides 1783 by NAT_4:9;
    1783 = 31*57 + 16; hence not 31 divides 1783 by NAT_4:9;
    1783 = 37*48 + 7; hence not 37 divides 1783 by NAT_4:9;
    1783 = 41*43 + 20; hence not 41 divides 1783 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1783 & n is prime
  holds not n divides 1783 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
