
theorem
  359 is prime
proof
  now
    359 = 2*179 + 1; hence not 2 divides 359 by NAT_4:9;
    359 = 3*119 + 2; hence not 3 divides 359 by NAT_4:9;
    359 = 5*71 + 4; hence not 5 divides 359 by NAT_4:9;
    359 = 7*51 + 2; hence not 7 divides 359 by NAT_4:9;
    359 = 11*32 + 7; hence not 11 divides 359 by NAT_4:9;
    359 = 13*27 + 8; hence not 13 divides 359 by NAT_4:9;
    359 = 17*21 + 2; hence not 17 divides 359 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 359 & n is prime
  holds not n divides 359 by XPRIMET1:14;
  hence thesis by NAT_4:14;
end;
