
theorem
  787 is prime
proof
  now
    787 = 2*393 + 1; hence not 2 divides 787 by NAT_4:9;
    787 = 3*262 + 1; hence not 3 divides 787 by NAT_4:9;
    787 = 5*157 + 2; hence not 5 divides 787 by NAT_4:9;
    787 = 7*112 + 3; hence not 7 divides 787 by NAT_4:9;
    787 = 11*71 + 6; hence not 11 divides 787 by NAT_4:9;
    787 = 13*60 + 7; hence not 13 divides 787 by NAT_4:9;
    787 = 17*46 + 5; hence not 17 divides 787 by NAT_4:9;
    787 = 19*41 + 8; hence not 19 divides 787 by NAT_4:9;
    787 = 23*34 + 5; hence not 23 divides 787 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 787 & n is prime
  holds not n divides 787 by XPRIMET1:18;
  hence thesis by NAT_4:14;
