
theorem
  587 is prime
proof
  now
    587 = 2*293 + 1; hence not 2 divides 587 by NAT_4:9;
    587 = 3*195 + 2; hence not 3 divides 587 by NAT_4:9;
    587 = 5*117 + 2; hence not 5 divides 587 by NAT_4:9;
    587 = 7*83 + 6; hence not 7 divides 587 by NAT_4:9;
    587 = 11*53 + 4; hence not 11 divides 587 by NAT_4:9;
    587 = 13*45 + 2; hence not 13 divides 587 by NAT_4:9;
    587 = 17*34 + 9; hence not 17 divides 587 by NAT_4:9;
    587 = 19*30 + 17; hence not 19 divides 587 by NAT_4:9;
    587 = 23*25 + 12; hence not 23 divides 587 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 587 & n is prime
  holds not n divides 587 by XPRIMET1:18;
  hence thesis by NAT_4:14;
