
theorem
  1787 is prime
proof
  now
    1787 = 2*893 + 1; hence not 2 divides 1787 by NAT_4:9;
    1787 = 3*595 + 2; hence not 3 divides 1787 by NAT_4:9;
    1787 = 5*357 + 2; hence not 5 divides 1787 by NAT_4:9;
    1787 = 7*255 + 2; hence not 7 divides 1787 by NAT_4:9;
    1787 = 11*162 + 5; hence not 11 divides 1787 by NAT_4:9;
    1787 = 13*137 + 6; hence not 13 divides 1787 by NAT_4:9;
    1787 = 17*105 + 2; hence not 17 divides 1787 by NAT_4:9;
    1787 = 19*94 + 1; hence not 19 divides 1787 by NAT_4:9;
    1787 = 23*77 + 16; hence not 23 divides 1787 by NAT_4:9;
    1787 = 29*61 + 18; hence not 29 divides 1787 by NAT_4:9;
    1787 = 31*57 + 20; hence not 31 divides 1787 by NAT_4:9;
    1787 = 37*48 + 11; hence not 37 divides 1787 by NAT_4:9;
    1787 = 41*43 + 24; hence not 41 divides 1787 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1787 & n is prime
  holds not n divides 1787 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
