
theorem
  2971 is prime
proof
  now
    2971 = 2*1485 + 1; hence not 2 divides 2971 by NAT_4:9;
    2971 = 3*990 + 1; hence not 3 divides 2971 by NAT_4:9;
    2971 = 5*594 + 1; hence not 5 divides 2971 by NAT_4:9;
    2971 = 7*424 + 3; hence not 7 divides 2971 by NAT_4:9;
    2971 = 11*270 + 1; hence not 11 divides 2971 by NAT_4:9;
    2971 = 13*228 + 7; hence not 13 divides 2971 by NAT_4:9;
    2971 = 17*174 + 13; hence not 17 divides 2971 by NAT_4:9;
    2971 = 19*156 + 7; hence not 19 divides 2971 by NAT_4:9;
    2971 = 23*129 + 4; hence not 23 divides 2971 by NAT_4:9;
    2971 = 29*102 + 13; hence not 29 divides 2971 by NAT_4:9;
    2971 = 31*95 + 26; hence not 31 divides 2971 by NAT_4:9;
    2971 = 37*80 + 11; hence not 37 divides 2971 by NAT_4:9;
    2971 = 41*72 + 19; hence not 41 divides 2971 by NAT_4:9;
    2971 = 43*69 + 4; hence not 43 divides 2971 by NAT_4:9;
    2971 = 47*63 + 10; hence not 47 divides 2971 by NAT_4:9;
    2971 = 53*56 + 3; hence not 53 divides 2971 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2971 & n is prime
  holds not n divides 2971 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
