
theorem
  2969 is prime
proof
  now
    2969 = 2*1484 + 1; hence not 2 divides 2969 by NAT_4:9;
    2969 = 3*989 + 2; hence not 3 divides 2969 by NAT_4:9;
    2969 = 5*593 + 4; hence not 5 divides 2969 by NAT_4:9;
    2969 = 7*424 + 1; hence not 7 divides 2969 by NAT_4:9;
    2969 = 11*269 + 10; hence not 11 divides 2969 by NAT_4:9;
    2969 = 13*228 + 5; hence not 13 divides 2969 by NAT_4:9;
    2969 = 17*174 + 11; hence not 17 divides 2969 by NAT_4:9;
    2969 = 19*156 + 5; hence not 19 divides 2969 by NAT_4:9;
    2969 = 23*129 + 2; hence not 23 divides 2969 by NAT_4:9;
    2969 = 29*102 + 11; hence not 29 divides 2969 by NAT_4:9;
    2969 = 31*95 + 24; hence not 31 divides 2969 by NAT_4:9;
    2969 = 37*80 + 9; hence not 37 divides 2969 by NAT_4:9;
    2969 = 41*72 + 17; hence not 41 divides 2969 by NAT_4:9;
    2969 = 43*69 + 2; hence not 43 divides 2969 by NAT_4:9;
    2969 = 47*63 + 8; hence not 47 divides 2969 by NAT_4:9;
    2969 = 53*56 + 1; hence not 53 divides 2969 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2969 & n is prime
  holds not n divides 2969 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
