
theorem
  151 is prime
proof
  now
    151 = 2*75 + 1; hence not 2 divides 151 by NAT_4:9;
    151 = 3*50 + 1; hence not 3 divides 151 by NAT_4:9;
    151 = 5*30 + 1; hence not 5 divides 151 by NAT_4:9;
    151 = 7*21 + 4; hence not 7 divides 151 by NAT_4:9;
    151 = 11*13 + 8; hence not 11 divides 151 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 151 & n is prime
  holds not n divides 151 by XPRIMET1:10;
  hence thesis by NAT_4:14;
end;
