
theorem
  853 is prime
proof
  now
    853 = 2*426 + 1; hence not 2 divides 853 by NAT_4:9;
    853 = 3*284 + 1; hence not 3 divides 853 by NAT_4:9;
    853 = 5*170 + 3; hence not 5 divides 853 by NAT_4:9;
    853 = 7*121 + 6; hence not 7 divides 853 by NAT_4:9;
    853 = 11*77 + 6; hence not 11 divides 853 by NAT_4:9;
    853 = 13*65 + 8; hence not 13 divides 853 by NAT_4:9;
    853 = 17*50 + 3; hence not 17 divides 853 by NAT_4:9;
    853 = 19*44 + 17; hence not 19 divides 853 by NAT_4:9;
    853 = 23*37 + 2; hence not 23 divides 853 by NAT_4:9;
    853 = 29*29 + 12; hence not 29 divides 853 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 853 & n is prime
  holds not n divides 853 by XPRIMET1:20;
  hence thesis by NAT_4:14;
