
theorem
  971 is prime
proof
  now
    971 = 2*485 + 1; hence not 2 divides 971 by NAT_4:9;
    971 = 3*323 + 2; hence not 3 divides 971 by NAT_4:9;
    971 = 5*194 + 1; hence not 5 divides 971 by NAT_4:9;
    971 = 7*138 + 5; hence not 7 divides 971 by NAT_4:9;
    971 = 11*88 + 3; hence not 11 divides 971 by NAT_4:9;
    971 = 13*74 + 9; hence not 13 divides 971 by NAT_4:9;
    971 = 17*57 + 2; hence not 17 divides 971 by NAT_4:9;
    971 = 19*51 + 2; hence not 19 divides 971 by NAT_4:9;
    971 = 23*42 + 5; hence not 23 divides 971 by NAT_4:9;
    971 = 29*33 + 14; hence not 29 divides 971 by NAT_4:9;
    971 = 31*31 + 10; hence not 31 divides 971 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 971 & n is prime
  holds not n divides 971 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
